how to find y intercept of an equation

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On their ain, y-intercepts aren't complicated at all—they're just points where the graph of the equation intersects with the Y-axis.^[1] Simply how are you lot supposed to find a y-intercept when you only accept a limited amount of info on hand? Thankfully, it's not nearly every bit hard as it looks. We'll walk you through all the major ways to find the y-intercept when you already have the slope and a point, two points, or just desire to apply a simple equation. With a piffling practice, you can brand quick work of any y-intercept problem that comes your manner.

1
Write down the slope and point. ^[2] The slope or "ascension over run" is a single number that tells yous how steep the line is. This type of trouble also gives you the (x,y) coordinate of one indicate along the graph. Skip to the other methods below if you don't have both these pieces of data.
- Case 1: A directly line with slope 2 contains the point (-iii,4). Find the y-intercept of this line using the steps below.
2

Learn the slope-intercept course of an equation. Whatsoever straight line tin can be written as an equation in the course y = mx + b. When the equation is in this form, the variable yard is the slope, and b is the y-intercept.

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three
Substitute the slope in this equation. Write the gradient-intercept equation, but instead of thou, utilise the slope of your line.
- Example one (cont.): y = m10 + b
  thou = slope = two
  y = iix + b
4
Replace x and y with the coordinates of the point. Any time you accept the coordinates of a single point on your line, you tin substitute those x and y coordinates for the x and y in your line equation. Practice this for the equation you've been working on.
- Example 1 (cont.): The point (3,4) is on this line. At this point, 10 = 3 and y = 4.
  Substitute these values into y = iix +b:
  4 = two(3) + b
v
Solve for b. Recall, b is the y-intercept of the line. At present that b is the simply variable in the equation, rearrange to solve for this variable and find the answer.
- Instance ane (cont.): 4 = 2(3) + b
  4 = 6 + b
  iv - half dozen = b
  -2 = b
  The y-intercept of this line is -2.
six
Write this as a coordinate bespeak. The y-intercept is the point where the line intersects with the y-centrality. Since the y-axis is located at x = 0, the x coordinate of the y-intercept is always 0.
- Instance 1 (cont.): The y-intercept is at y = -2, so the coordinate betoken is (0, -2).
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ane
Write down the coordinates of both points. ^[three] This method covers problems that merely tell y'all two points on a straight line.^[4] Write each point coordinate down in (x,y) class.
- Example ii: A straight line passes through points (-ane, two) and (iii, -4). Find the y-intercept of this line using the steps below.
2
Calculate the ascension and run. Slope is a measure of how much vertical distance the line moves for each unit of horizontal distance. Y'all may have heard this described as "rise over run" ( ${\frac {rising}{run}}$ ).^[5] Hither'southward how to find these two quantities from 2 points:
- "Ascension" is the change in vertical distance, or the deviation betwixt the y-values of the ii points.
- "Run" is the change in horizontal distance, or the difference between 10-values of the same two points.
- Example 2 (cont.): The y-values of the two points are two and -4, then the rise is (-4) - (2) = -vi.
  The x-values of the 2 points (in the same lodge) are 1 and 3, and then the run is 3 - 1 = 2.
3
Separate ascension by run to detect the gradient. Now that you know these two values, plug them into " ${\frac {rise}{run}}$ " to detect the slope of the line.
- Case ii (cont.): $slope={\frac {rise}{run}}={\frac {-6}{two}}=$ -3.
iv

Review the slope-intercept form. You can describe a straight line with the formula y = mx + b, where g is the slope and b is the y-intercept.^[6] Now that we know the gradient chiliad and a point (ten,y), we tin apply this equation to solve for b, the y-intercept.
five
Fit the slope and betoken into the equation. Take the equation in slope-intercept grade and supervene upon m with the slope you calculated. Replace the ten and y terms with the coordinates of a single point on the line.^[vii] It doesn't affair which point you use.
- Example 2 (cont.): y = mx + b
  Slope = thou = -3, so y = -3x + b
  The line includes a point with (10,y) coordinates (1,two), and so 2 = -3(ane) + b.
half-dozen
Solve for b. Now the only variable left in the equation is b, the y-intercept. Rearrange the equation so b is on one side, and y'all take your answer.^[8] Call back, the y-intercept e'er has an x-coordinate of 0.
- Instance 2 (cont.): 2 = -3(1) + b
  ii = -3 + b
  5 = b
  The y-intercept is at (0,five).
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Write down the equation of the line. If you already have the equation of the line, you can detect the y-intercept with a little algebra.^[9]
- Example 3: What is the y-intercept of the line ten + 4y = 16?
- Notation: Example iii is a directly line. Meet the end of this section for an instance of a quadratic equation (with a variable raised to the power of 2).
2
Substitute 0 for x. The y-axis is a vertical line along x = 0. This means whatever point on the y-axis has an x-coordinate of 0, including the y-intercept of the line. Plug in 0 for x in the line equation.
- Example 3 (cont.): 10 + 4y = 16
  x = 0
  0 + 4y = sixteen
  4y = sixteen
iii
Solve for y. The respond is the y-intercept of the line.
- Example 3 (cont.): 4y = 16
  ${\frac {4y}{4}}={\frac {sixteen}{4}}$
  y = iv.
  The y-intercept of the line is 4.
4

Confirm past graphing (optional) . To cheque your reply, graph the equation as neatly as you can. The point where the line crosses the y-axis is the y-intercept.
v

Find the y-intercept for a quadratic equation. A quadratic equation includes a variable (10 or y) raised to the power of 2. You can solve for y with the aforementioned exchange, only since the quadratic describes a curve, it could intercept the y-axis at 0, 1, or two points. This means you may stop up with 0, ane, or 2 answers.

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Question

How do you find the x-intercept in y = mx + b?

David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a individual tutoring company based in Los Angeles, California. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, also every bit college admissions counseling and test preparation for the SAT, Human activity, ISEE, and more. Later attaining a perfect 800 math score and a 690 English language score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Available's caste in Concern Administration. Additionally, David has worked as an teacher for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

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Expert Reply

Discover the x-intercept by plugging in 0 for the value of y. The x-intercept will equal whatever value comes out at the other end of the equation.
Question

What practise you mean by x-intercept in math?

David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring visitor based in Los Angeles, California. With over x years of teaching feel, David works with students of all ages and grades in various subjects, likewise as college admissions counseling and exam training for the Saturday, ACT, ISEE, and more. Later on attaining a perfect 800 math score and a 690 English score on the Saturday, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Available's degree in Business Administration. Additionally, David has worked as an teacher for online videos for textbook companies such as Larson Texts, Large Ideas Learning, and Big Ideas Math.

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Expert Respond

The x-intercept is merely wherever the graph crosses the x-centrality (the straight, horizontal line that cuts through the heart of the graph).
Question

If I have (3, -12) equally my points and an x-intercept of i, what would the y-intercept exist?

Solve past using Method two above. You need 2 points to use that method. One betoken is given as (3,-12). The second indicate is the given x-intercept, which is (i,0).
Question

If I am only given 1 specific indicate, how tin I convert it into slope intercept form?

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Customs Reply

You can't accept only 1 point. Imagine you're standing in the middle of your neighborhood street and accept no where to get. No management, no distance, etc. You don't need to become to your friend's house or to school. That is an example of having only one point without any other point to go to so there'south no line. Thus, no equation. And more importantly, no math to work out.
Question

I do not go the last function of method 2, can you explicate?

Using the "slope-intercept" course of the line's equation (y = mx + b), you solve for b (which is the y-intercept you lot're looking for). Substitute the known slope for m, and substitute the known point's coordinates for 10 and y, respectively, in the slope-intercept equation. That will let you lot find b. In the example in Method 2, the calculated slope is -3, so yard becomes -3. The known signal is given as (1,2), then x in the equation becomes 1, and y becomes 2. Thus, the gradient-intercept equation becomes 2 = -iii(1) + b. So two = -three + b, and b = v. That'south the y-intercept.
Question

What do I do if the only thing on the other side of the = is a variable?

If you mean that the only thing on the "ten" side of the equation is ten (so that y = x), that indicates a slope (m) of one and a y-intercept (b) of zero.
Question

How do I find the y intercept when it is not numbered and obviously a decimal?

Assuming by numbered yous mean whole number, it doesn't matter, the method is the same in both cases.
Question

How do I find the y-intercept if 3x - y = half-dozen?

The graph crosses the y-axis when x=0, and so substitute 0 for x in this equation, and solve for y: y is -6. Since y is -half dozen when x is 0, the y-intercept is -6.
Question

How do I find the y-intercept if the only given information is the slope and no graph or point(southward) specified?

You would have to exist given more than information than only the slope in society to discover the y-intercept.
Question

How practice I find the gradient for this and then the y-intercept (0,0) and (iv,-3)?

The slope has a numerator consisting of the difference between any two ten values on the line and a denominator consisting of the difference betwixt the two corresponding y values. In this case the slope is (four - 0) / (-three - 0), or 4 / -three, which equals -4/3. The y-intercept is the y-value when x=0. In this case, nosotros are told that the line passes through the point (0,0), which means that the y-intercept is zero.

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For more complicated equations, effort to isolate the terms containing y onto i side of the equation.
Some countries apply a c or another variable instead of b in the equation y = mx + b.^[x] This doesn't alter the meaning; information technology's just a dissimilar tradition.
When calculating slope between ii points, you tin can subtract the x and y coordinates from each other in either order, as long as you put the points in the same club for both rise and run.^[xi] For example, the slope between (1, 12) and (3, 7) tin exist calculated in 2 different means:

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Article Summary 10

To notice the y intercept using the equation of the line, plug in 0 for the x variable and solve for y. If the equation is written in the gradient-intercept form, plug in the slope and the x and y coordinates for a bespeak on the line to solve for y. If you don't know the slope, calculate information technology by dividing the rise of the line past the run. If you want to find the y-intercept if y'all only know 2 points along the line, keep reading the article!

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