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ACT Math : x and y Intercept

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Example Questions

Example Question #4 : How To Find X Or Y Intercept

Given the linear equation below, what are the x- and y-intercepts, respectively?

Possible Answers:

$(3,0)\ \text{and}\ (0,3)$

$(-3,0)\ \text{and}\ (0,3)$

$(-1,0)\ \text{and}\ (0,3)$

$(1,0)\ \text{and}\ (0,1)$

$(-3,0)\ \text{and}\ (0,-1)$

Correct answer:

$(-3,0)\ \text{and}\ (0,3)$

Explanation:

To find the x-intercept we will need to plug in zero for the y-value.

-3+0-x=0

-x=3

x=-3

The x-intercept will be (-3,0) .

To find the y-intercept we will need to plug in zero for the x-value.

-3+y-0=0

y=3

The y-intercept will be (0,3) .

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Example Question #5 : How To Find X Or Y Intercept

At what point do the lines $\small y=\frac{1}{4}x+7$ and $\small y=4x + 7$ intersect?

Possible Answers:

$(0,-7)$

$They\ do\ not\ intersect$

$(0,0)$

$(0,7)$

$(7,0)$

Correct answer:

$(0,7)$

Explanation:

Short way:

The lines intersect somewhere because they have different slopes. Because they have the same y-intercept, they must intersect at that point.

Long way using substitution:

$\small y=\frac{1}{4}x+7$

$\small y-7 = \frac{1}{4}x$

$\small x = 4y - 28$

Plug this into $\small y=-4x+7$

$\small y=-4(4y-28)+7$

$\small y=-16y+112+7$

$\small 17y=119$

$\small y=7$

Find $\small x$

$\small x=4(7)-28=0$

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Example Question #6 : How To Find X Or Y Intercept

Find the -intercept(s) for the following equation:

y = 2x^2 -18

Possible Answers:

(3,0)

(3,0), (-3,0)

(-3,0)

(-18,0)

$(\frac{9}{2},0)$

Correct answer:

(3,0), (-3,0)

Explanation:

To find the intercepts, is set equal to . This yields:

18 = 2x^2

x^2 = 9

And finally $x=\pm3$

It is important to realize that both x=3 and x=-3 must be included because -3^2 is also equal to . Finally, these are put into their point forms, (3,0) and (-3,0) .

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Example Question #12 : X And Y Intercept

What is the largest x-intercept of 2y = 2x^2 +16x + 30 ?

Possible Answers:

There are no x intercepts for this equation.

Correct answer:

Explanation:

To find the x-intercepts of an equation, you can just set the y value of the equation equal to zero. Thus you get, for our data:

0 = 2x^2 +16x + 30

Now, you can divide everything by to simplify your equation:

0 = x^2 +8x + 15

Luckily, this is an easy equation to factor:

0=(x+3)(x+5)

Based on this, you know that the two intercepts must be where x=-3 and x=-5 . Thus, the largest intercept is .

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Example Question #13 : X And Y Intercept

What is the sum of the x-intercepts of y=3x^3-75x ?

Possible Answers:

Correct answer:

Explanation:

y=3x^3-75x

To find the x-intercepts of an equation, you can set its y value equal to zero. Thus, you get for our equation:

0=3x^3-75x

Now, factor out all common factors:

0=3x(x^2-25)

From this, you can further factor:

0=3x(x-5)(x+5)

Thus, the x-intercepts of our equation are ,, and . The sum of these values is .

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Example Question #11 : How To Find X Or Y Intercept

What is the $y\textup{ intercept}$ of the following equation: y = 2x + 7 ?

Possible Answers:

$\frac{2}{7}$

$\frac{7}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

The y-intercept is the constant at the end of the equation. Thus for our equation the y-intercept is 7

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Example Question #13 : How To Find X Or Y Intercept

What is the -intercept of the following linear equation:
y = -2x + 5 ?

Give your answer as an ordered pair.

Possible Answers:

$\left(-\frac{5}{2},0\right)$

$\left(0, \frac{5}{2}\right)$

$\left(\frac{5}{2}, 0\right)$

(0,5)

(0,-5)

Correct answer:

$\left(\frac{5}{2}, 0\right)$

Explanation:

The x-intercept is the value of the linear equation with y = 0 (this means the line will be on the x-axis when y is zero).

Thus we plug 0 in for y and solve for x.

$\\0 = -2x + 5 \\ \newline 2x = 5 \\ \newline x = \frac{5}{2}$ .

Now put it in an ordered pair, remember y = 0:
$\left(\frac{5}{2}, 0\right)$

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Example Question #14 : How To Find X Or Y Intercept

What is the and intercepts of the linear equation given by:
y = 7x + 8 ?

Possible Answers:

$(0,-8),\left(\frac{8}{7},0\right)$

$(0,8), \left(-\frac{8}{7},0\right)$

(0,0),(0,8)

(-8,7),(-7,8)

$\left(0,\frac{7}{8}\right),(8,0)$

Correct answer:

$(0,8), \left(-\frac{8}{7},0\right)$

Explanation:

To find the and intercept of a linear equation, find the points where and are equal to zero.

To do this, plug in zero for either variable and then solve for the other.

$\\0 = 7x +8 \newline y = 7*0 + 8$

this yields:

$(0,8), \left(-\frac{8}{7},0\right)$

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Example Question #13 : X And Y Intercept

What is the and intercepts of the following linear equation:

y = -8x +3

Possible Answers:

(0,3)

$\left(\frac{3}{8},0\right)$

(3,0)

$\left(0,-\frac{8}{3}\right)$

(0,3)

$\left(-\frac{3}{8},0\right)$

(0,-8)

(-3,0)

(0,3)

Correct answer:

(0,3)

$\left(\frac{3}{8},0\right)$

Explanation:

To find the and intercepts of an equation, set each variable to zero (one at a time) and solve for the other variable.
$\\0 = -8x + 3 \newline -3 = -8x \newline \frac{3}{8} = x$

Next, set to zero:

$\\y = -8(0) +3 \newline y = 3$
Now put these two sets of points into two ordered pairs:

(0,3)

$\left(\frac{3}{8},0\right)$

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ACT Math : x and y Intercept

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #4 : How To Find X Or Y Intercept

Example Question #5 : How To Find X Or Y Intercept

Example Question #6 : How To Find X Or Y Intercept

Example Question #12 : X And Y Intercept

Example Question #13 : X And Y Intercept

Example Question #11 : How To Find X Or Y Intercept

Example Question #13 : How To Find X Or Y Intercept

Example Question #14 : How To Find X Or Y Intercept

Example Question #13 : X And Y Intercept

All ACT Math Resources

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