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ACT Math : ACT Math

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Example Questions

Example Question #96 : Algebra

What is the slope of the line defined by the equation 3x + 5y = y + 20 ?

Possible Answers:

$\frac{4}{3}$

$\frac{1}{3}$

$-\frac{3}{4}$

Correct answer:

$-\frac{3}{4}$

Explanation:

The easiest way to find the slope of a line based on its equation is to put it into the form y=mx+b . In this form, you know that is the slope.

Start with your original equation 3x + 5y = y + 20 .

Now, subtract from both sides:

3x + 4y = 20

Next, subtract from both sides:

4y = 20-3x

Finally, divide by :

$y = 5-\frac{3}{4}x$

This is the same as:

$y = -\frac{3}{4}x + 5$

Thus, the slope is $-\frac{3}{4}$ .

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Example Question #731 : Act Math

What is the slope of the line represented by the equation 4y - 5 = 12x ?

Possible Answers:

1/3

-5/12

Correct answer:

Explanation:

The slope of an equation can be calculated by simplifying the equation to the slope-intercept form y = mx + b , where m=slope.

Since 4y - 5 = 12x , we can solve for y. In shifting the 5 to the other side, we are left with 4y = 12x + 5 .

This can be further simplified to

$y = 3x + \frac{5}{4}$ , leaving us with the y = mx + b slope intercept form.

In this scenario, m=3 , so slope .

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Example Question #731 : Act Math

Find the slope of the line 6X – 2Y = 14

Possible Answers:

-3

-6

Correct answer:

Explanation:

Put the equation in slope-intercept form:

y = mx + b

-2y = -6x +14

y = 3x – 7

The slope of the line is represented by M; therefore the slope of the line is 3.

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Example Question #3 : Coordinate Geometry

What line goes through the points (1, 3) and (3, 6)?

Possible Answers:

–3x + 2y = 3

2x – 3y = 5

–2x + 2y = 3

3x + 5y = 2

4x – 5y = 4

Correct answer:

–3x + 2y = 3

Explanation:

If P₁(1, 3) and P₂(3, 6), then calculate the slope by m = rise/run = (y₂ – y₁)/(x₂ – x₁) = 3/2

Use the slope and one point to calculate the intercept using y = mx + b

Then convert the slope-intercept form into standard form.

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Example Question #4 : Coordinate Geometry

What is the slope-intercept form of $\dpi{100} \small 8x-2y-12=0$ ?

Possible Answers:

$\dpi{100} \small y=-4x+6$

$\dpi{100} \small y=4x-6$

$\dpi{100} \small y=4x+6$

$\dpi{100} \small y=-2x+3$

$\dpi{100} \small y=2x-3$

Correct answer:

$\dpi{100} \small y=4x-6$

Explanation:

The slope intercept form states that $\dpi{100} \small y=mx+b$ . In order to convert the equation to the slope intercept form, isolate $\dpi{100} \small y$ on the left side:

$\dpi{100} \small 8x-2y=12$

$\dpi{100} \small -2y=-8x+12$

$\dpi{100} \small y=4x-6$

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Example Question #5 : Coordinate Geometry

A line is defined by the following equation:

7x+28y=84

What is the slope of that line?

Possible Answers:

$-\frac{1}{4}$

$\frac{1}{4}$

Correct answer:

$-\frac{1}{4}$

Explanation:

The equation of a line is

y=mx + b where m is the slope

Rearrange the equation to match this:

7x + 28y = 84

28y = -7x + 84

y = -(7/28)x + 84/28

y = -(1/4)x + 3

m = -1/4

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Example Question #732 : Act Math

If the coordinates (3, 14) and (–5, 15) are on the same line, what is the equation of the line?

Possible Answers:

$y=-\frac{1}{8}x+13.625$

y=-8x-38

$y=\frac{1}{8}x+14.375$

y=-8x+38

$y=-\frac{1}{8}x+14.375$

Correct answer:

$y=-\frac{1}{8}x+14.375$

Explanation:

First solve for the slope of the line, m using y=mx+b

m = (y2 – y1) / (x2 – x1)

= (15 – 14) / (–5 –3)

= (1 )/( –8)

=–1/8

y = –(1/8)x + b

Now, choose one of the coordinates and solve for b:

14 = –(1/8)3 + b

14 = –3/8 + b

b = 14 + (3/8)

b = 14.375

y = –(1/8)x + 14.375

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Example Question #7 : Coordinate Geometry

What is the equation of a line that passes through coordinates $\dpi{100} \small (2,6)$ and $\dpi{100} \small (3,5)$ ?

Possible Answers:

$\dpi{100} \small y=2x+4$

$\dpi{100} \small y=x+7$

$\dpi{100} \small y=2x-4$

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

$\dpi{100} \small y=3x+2$

Correct answer:

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

Explanation:

Our first step will be to determing the slope of the line that connects the given points.

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-5}{2-3}=\frac{1}{-1}=-1$

Our slope will be . Using slope-intercept form, our equation will be y=(-1)x+b . Use one of the give points in this equation to solve for the y-intercept. We will use $\dpi{100} \small (2,6)$ .

6=(-1)(2)+b

6=-2+b

8=b

Now that we know the y-intercept, we can plug it back into the slope-intercept formula with the slope that we found earlier.

y=(-1)x+8

y=-x+8

This is our final answer.

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Example Question #8 : Coordinate Geometry

Which of the following equations does NOT represent a line?

Possible Answers:

x+y=10

5y=10

x^2+y=10

x=10

x-y=10

Correct answer:

x^2+y=10

Explanation:

The answer is x^2+y=10 .

A line can only be represented in the form x=z or y=mx+b , for appropriate constants , , and . A graph must have an equation that can be put into one of these forms to be a line.

x^2+y=10 represents a parabola, not a line. Lines will never contain an x^2 term.

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Example Question #9 : Coordinate Geometry

Let y = 3x – 6.

At what point does the line above intersect the following:

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

Possible Answers:

They intersect at all points

(0,–1)

(–3,–3)

They do not intersect

(–5,6)

Correct answer:

They intersect at all points

Explanation:

If we rearrange the second equation it is the same as the first equation. They are the same line.

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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #96 : Algebra

Example Question #731 : Act Math

Example Question #731 : Act Math

Example Question #3 : Coordinate Geometry

Example Question #4 : Coordinate Geometry

Example Question #5 : Coordinate Geometry

Example Question #732 : Act Math

Example Question #7 : Coordinate Geometry

Example Question #8 : Coordinate Geometry

Example Question #9 : Coordinate Geometry

All ACT Math Resources

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