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

David Jia
Academic Tutor
David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private 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, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

Academic Tutor

Expert Answer

Find 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.

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Question

What do you mean by x-intercept in math?

David Jia
Academic Tutor
David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private 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, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

David Jia

Academic Tutor

Expert Answer

The x-intercept is just wherever the graph crosses the x-axis (the straight, horizontal line that cuts through the middle of the graph).

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Question

If I have (3, -12) as my points and an x-intercept of one, what would the y-intercept be?

Donagan

Top Answerer

Solve by using Method 2 above. You need two points to use that method. One point is given as (3,-12). The second point is the given x-intercept, which is (1,0).

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If I am only given one specific point, how can I convert it into slope intercept form?

Technist

Community Answer

You can't have only one point. Imagine you're standing in the middle of your neighborhood street and have no where to go. No direction, no distance, etc. You don't need to go 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's no line. Thus, no equation. And more importantly, no math to work out.

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Question

I do not get the last part of method 2, can you explain?

Donagan

Top Answerer

Using the "slope-intercept" form of the line's equation (y = mx + b), you solve for b (which is the y-intercept you're looking for). Substitute the known slope for m, and substitute the known point's coordinates for x and y, respectively, in the slope-intercept equation. That will let you find b. In the example in Method 2, the calculated slope is -3, so m becomes -3. The known point is given as (1,2), so x in the equation becomes 1, and y becomes 2. Thus, the slope-intercept equation becomes 2 = -3(1) + b. So 2 = -3 + b, and b = 5. That's the y-intercept.

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

Donagan

Top Answerer

If you mean that the only thing on the "x" side of the equation is x (so that y = x), that indicates a slope (m) of 1 and a y-intercept (b) of zero.

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Question

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

Community Answer

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

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Question

How do I find the y-intercept if 3x - y = 6?

Community Answer

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

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

Donagan

Top Answerer

You would have to be given more information than just the slope in order to find the y-intercept.

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Question

How do I find the slope for this and then the y-intercept (0,0) and (4,-3)?

Donagan

Top Answerer

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

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Question

What if the slope is undefined?

Donagan

Top Answerer

If a slope is said to be "undefined," that means that the slope is infinite, which in turn means that the line is vertical (or parallel to the y-axis).

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Question

Where is the y-axis on the Cartesian plane?

Donagan

Top Answerer

The y-axis is the vertical line that passes through the origin. It is the series of all points where x = 0.

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Question

What if my problem looks like 4y = 3?

Aiden Chester

Community Answer

OK, let's put the equation into slope-intercept form (y = ax+b), where we know b is the y-intercept. If we divide both sides by 4, then we get y = 3/4. There are 0 x's, so ax = 0x. That leaves us with y = 0x+3/4, where b = 3/4. This does make sense, because 0x would just cancel out to 0, leaving us with our original equation of y = 3/4. If b is the y-intercept value, then the y-intercept is at (0, 3/4)! You can check a graph of y = 3/4 to make sure.

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Question

if you know the slope how do you find the y intercept?

Community Answer

For example, the slope of your line is 2 and a point that goes on your line is (2,6), then substite the values with the equation y=mx+b, where the m is the gradient and the the b is the y intercept. y=mx+b, y=2x+b. Substitute the coordinate points. 6=2(2)+b, 6=4+b. Now, you need to get b alone on one side, so rearrange the equation. 6=4+b, 6-4=b, 6-4=2, 2 is the y-intercept.

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Does an answer of zero mean the graph is horizontal?

Community Answer

If x were to be zero, then the line would be horizontal. If y is zero, it just crosses through the origin.

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Question

How do I find the Y intercept if I know the points?

Community Answer

Let’s say the points are (2,6) and (-3,-4). Subtracting the y-value of one point from the y-value of the other we get -4-6=-10. Subtracting the x-value of the same point from the x-value of the other, we get -3-2=-5. The slope of the line, m, equals (-10/-5)=+2. So m=2. Remembering that the general equation of a line is y=mx+b, this line’s equation is y=2x+b. We also have the two points given at the beginning and we can use either one to enter the x and y values of the point into the equation, so 6=2(2)+b. So we solve for b. b=6-4=2, which is the y-intercept we were looking for.

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How do I find the Y intercept when it does not cross or touch the Y axis?

Community Answer

In that case, keep counting the boxes until you get to a spot where it would intercept with the y axis.

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Question

If the gradient of a line is -4 and it has an x-intercept of 3, what's the y-intercept of the line?

Cabbache

Community Answer

The equation of a line is y = mx + c where c is the y-intercept. We are given m = -4, so the equation is y = -4x + c. We know that the line has an x-intercept of 3, which means the line passes through point 3,0. This means that when y = 0, then x = 3 so 0 = -4(3) + c. From that we can find c = 7, which is the y-intercept.

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Question

How do I find the y intercept when a line passes through the origin if I have x value and slope value?

Donagan

Top Answerer

If the line passes through the origin, that means the y intercept is zero.

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y = 1/2. What is the y-intercept and slope?

Community Answer

When y equals a constant (such as 1/2), the graph consists of a straight, horizontal line that crosses the y-axis at the value of the constant. So here the line parallels the x-axis, which means its slope is 0, and it intercepts the y-axis at +1/2.

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Question

What is the y-intercept of a line with a slope of -3/2 and an x-intercept of (4,0)?

Community Answer

Plug the values (4,0) into the slope-intercept form of the equation, y = mx + b, given that m = -3/2: 0 = (-3/2)(4) + b. Then 0 = -6 + b, and 6 = b. So the y-intercept (b) is 6.

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