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ACT Math : Algebra

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Example Questions

Example Question #1 : X And Y Intercept

What is the $\dpi{100} \small x$ -coordinate of the point in the standard $\dpi{100} \small (x,y)$ coordinate plane at which the two lines $\dpi{100} \small y=4x+8$ and $\dpi{100} \small y=3x-7$ intersect?

Possible Answers:

$\dpi{100} \small 15$

$\dpi{100} \small 12$

$\dpi{100} \small 1$

$\dpi{100} \small -7$

$\dpi{100} \small -15$

Correct answer:

$\dpi{100} \small -15$

Explanation:

$\dpi{100} \small 4x+8=3x-7$

$\dpi{100} \small x+8=-7$

$\dpi{100} \small x=-15$

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Example Question #2 : X And Y Intercept

What is the -intercept of the line in the standard (x,y) coordinate plane that goes through the points (-4,8) and (4,2) ?

Possible Answers:

Correct answer:

Explanation:

The answer is .

The slope of the line is determined by calculating the change in over the change in x, (8-2)/(-4-4) = -(6/8) .

The point-slope form of the equation for the line is then

(y-2) = -(6/8)*(x-4) . The -intercept is determined by setting x=0 and solving for . This simplifies to y=5 which shows that is the -interecept.

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Example Question #1 : How To Find X Or Y Intercept

What are the and -intercepts of the line defined by the equation:

y = 3x + 6

Possible Answers:

(2,0) (2,-6)

(0,-6) (0,0)

(0,0) (0,0)

(-2,0) (0,6)

(0,6) (2,0)

Correct answer:

(-2,0) (0,6)

Explanation:

To find the intercepts of a line, we must set the and values equal to zero and then solve.

0 = 3x +6

-6 = 3x

x = -2

(-2, 0)

y = 3 (0) + 6

y = 6

(0, 6)

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Example Question #1 : How To Find X Or Y Intercept

In the standard (x, y) coordinate plane, a circle has the equation x^2+y^2=64 . At what points does the circle intersect the x-axis?

Possible Answers:

$(16,0)\ \text{and}\ (-16,0)$

$(64,0)\ \text{and}\ (-64,0)$

$(4,0)\ \text{and}\ (-4,0)$

$(8,0)\ \text{and}\ (-8,0)$

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

Correct answer:

$(8,0)\ \text{and}\ (-8,0)$

Explanation:

The generic equation of a circle is (x - x₀)² + (y - y₀)² = r², where (x₀, y₀) are the coordinates of the center and r is the radius.

x^2+y^2=64

In this case, the circle is centered at the origin with a radius of 8. Therefore the circle hits all points that are a distance of 8 from the origin, which results in coordinates of (8,0) and (-8,0) on the x-axis.

Act_math_172_01

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Example Question #3 : How To Find X Or Y Intercept

What is the y-intercept of a line that passes through the point (-5,8) with slope of ?

Possible Answers:

(0,4)

(0,-2)

(2,0)

(0,0)

(0,2)

Correct answer:

(0,-2)

Explanation:

Point-slope form follows the format y - y₁ = m(x - x₁).

Using the given point and slope, we can use this formula to get the equation y - 8 = -2(x + 5).

From here, we can find the y-intercept by setting x equal to zero and solving.

y - 8 = -2(0 + 5)

y - 8 = -2(5) = -10

y = -2

Our y-intercept will be (0,-2).

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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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ACT Math : Algebra

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : X And Y Intercept

Example Question #2 : X And Y Intercept

Example Question #1 : How To Find X Or Y Intercept

Example Question #1 : How To Find X Or Y Intercept

Example Question #3 : How To Find X Or Y Intercept

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

All ACT Math Resources

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