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ACT Math : x and y Intercept

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Example Questions

Example Question #1 : X And Y Intercept

Find the slope of the following line: 6x – 4y = 10

Possible Answers:

5/2

1.5

–1.5

–5/2

Correct answer:

1.5

Explanation:

Putting the equation in y = mx + b form we obtain y = 1.5x – 2.5.

The slope is 1.5.

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Example Question #142 : Coordinate Plane

What is the x-intercept of the line in the standard $\left ( x,y \right )$ coordinate plane for the following equation?

$\frac{1}{2}y+10=6x-2$

Possible Answers:

-24

$\frac{4}{3}$

Correct answer:

Explanation:

This question is asking us to find the x-intercept. Remember that the y-value is equal to zero at the x-intercept. Substitute zero in for the y-variable in the equation and solve for the x-variable.

$\frac{1}{2}(0)+10=6x-2$

10=6x-2

Add 2 to both sides of the equation.

10+2=6x-2+2

12=6x

Divide both sides of the equation by 6.

$\frac{12}{6}=\frac{6x}{6}$

x=2

The line crosses the x-axis at 2.

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Example Question #1 : How To Find The Equation Of A Curve

What is the equation of a line that has an x-intercept of 4 and a y-intercept of -6?

Possible Answers:

$y=\frac{3}{2}x-6$

$y=\frac{3}{2}x+4$

$y=\frac{2}{3}x+4$

$y=\frac{3}{2}x+6$

$y=\frac{2}{3}x-6$

Correct answer:

$y=\frac{3}{2}x-6$

Explanation:

The equation of a line can be written in the following form:

y=mx+b

In this formula, m is the slope, and b represents the y-intercept. The problem provides the y-intercept; therefore, we know the following information:

b = -6

We can calculate the slope of the line, because if any two points on the function are known, then the slope can be calculated. Generically, the slope of a line is defined as the function's rise over run, or more technically, the changes in the y-values over the changes in the x-values. It is formally written as the following equation:

$\text{Slope}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The problem provides the two intercepts of the line, which can be written as $\left ( 4,0\right )$ and $\left ( 0,-6\right )$ . Substitute these points into the equation for slope and solve:

$\text{Slope}=\frac{(-6) - 0}{0-4}$

$\text{Slope}=\frac{-6}{-4}$

$\text{Slope}=\frac{3}{2}$ .

Substitute the calculated values into the general equation of a line to get the correct answer:

$y=\frac{3}{2}x-6$ .

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

What are the y and x intercepts of the given equation, respectively?

y = 2x – 2

Possible Answers:

(0, –2), (1, 0)

(0, 0), (0, 0)

(0, –2), (2, 0)

(0, –2), (–2, 0)

(0, 2), (2, 0)

Correct answer:

(0, –2), (1, 0)

Explanation:

The equation is already in slope-intercept form. The y-intercept is (0, –2). Plug in 0 for y and we get the x intercept of (1, 0)

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

What is the x-intercept of the following line?

y = –3x + 12

Possible Answers:

–4

–1/4

1/4

Correct answer:

Explanation:

The x-intercept occurs when the y-coordinate = 0.

y = –3x + 12

0 = –3x + 12

3x = 12

x = 12/3 = 4

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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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ACT Math : x and y Intercept

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : X And Y Intercept

Example Question #142 : Coordinate Plane

Example Question #1 : How To Find The Equation Of A Curve

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

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

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

All ACT Math Resources

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