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ACT Math : ACT Math

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Example Questions

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

Which of the following is the equation of a line between the points (0,3) and (4,15) ?

Possible Answers:

y-3x=3

y+2x=12

2x - 3y = 3

4x + 3y = 4

3x - 2y = 13

Correct answer:

y-3x=3

Explanation:

Since you have y-intercept, this is very easy. You merely need to find the slope. Then you can use the form y=mx+b to find one version of the line.

The slope is:

$\frac{rise}{run} = \frac{y_1-y_0}{x_1-x_0}$

Thus, for the points (0,3) and (4,15) , it is:

$\frac{15-3}{4-0}= \frac{12}{4}=3$

Thus, one form of our line is:

y=3x + 3

If you move the to the left side, you get:

y-3x=3 , which is one of your options.

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Example Question #2 : How To Find The Equation Of A Line

What is an equation of the line going through points (4,8) and (6,10) ?

Possible Answers:

6x + 3y = 12

x-y=4

4y-4x=16

4x - 2y = 10

2x + 3y = 4

Correct answer:

4y-4x=16

Explanation:

If you have two points, you can always use the point-slope form of a line to find your equation. Recall that this is:

y-y_0=m(x - x_0)

You first need to find the slope, though. Recall that this is:

$\frac{rise}{run} = \frac{y_1-y_0}{x_1-x_0}$

For the points (4,8) and (6,10) , it is:

$\frac{10-8}{6-4}=\frac{2}{2} = 1$

Thus, you can write the equation using either point:

y-8=1(x-4)

y-x=4

Now, notice that one of the options is:

4y-4x=16

This is merely a multiple of the equation we found, so it is fine!

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Example Question #3 : How To Find The Equation Of A Line

Given the graph of the line below, find the equation of the line.

Act_math_160_04

Possible Answers:

$y=\frac{10}{3}x-4$

y=x-4

y=-x

y=-5x-4

Correct answer:

$y=\frac{10}{3}x-4$

Explanation:

To solve this question, you could use two points such as (1.2,0) and (0,-4) to calculate the slope which is 10/3 and then read the y-intercept off the graph, which is -4.

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Example Question #4 : How To Find The Equation Of A Line

Which line passes through the points (0, 6) and (4, 0)?

Possible Answers:

y = 2/3 + 5

y = 2/3x –6

y = 1/5x + 3

y = –3/2 – 3

y = –3/2x + 6

Correct answer:

y = –3/2x + 6

Explanation:

P₁ (0, 6) and P₂ (4, 0)

First, calculate the slope: m = rise ÷ run = (y₂ – y₁)/(x₂– x₁), so m = –3/2

Second, plug the slope and one point into the slope-intercept formula:

y = mx + b, so 0 = –3/2(4) + b and b = 6

Thus, y = –3/2x + 6

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Example Question #741 : Act Math

Let W and Z be the points of intersection between the parabola whose graph is y = –x² – 2x + 3, and the line whose equation is y = x – 7. What is the length of the line segment WZ?

Possible Answers:

7√2

4√2

Correct answer:

7√2

Explanation:

First, set the two equations equal to one another.

–x² – 2x + 3 = x – 7

Rearranging gives

x² + 3x – 10 = 0

Factoring gives

(x + 5)(x – 2) = 0

The points of intersection are therefore W(–5, –12) and Z(2, –5)

Using the distance formula gives 7√2

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Example Question #742 : Act Math

In an xy-plane, what is the length of a line connecting points at (–2,–3) and (5,6)?

Possible Answers:

9.3

7.5

12.5

11.4

Correct answer:

11.4

Explanation:

Use the distance formula:

D = √((y₂ – y₁)² + (x₂ – x₁)²)

D = √((6 + 3)² + (5 + 2)²)

D = √((9)² + (7)²)

D = √(81 + 49)

D = √130

D = 11.4

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Example Question #743 : Act Math

What is the distance between points $\dpi{100} \small A$ and $\dpi{100} \small B$ , to the nearest tenth?

Possible Answers:

$\dpi{100} \small 5.0$

$\dpi{100} \small 3.2$

$\dpi{100} \small 6.4$

$\dpi{100} \small 7.8$

$\dpi{100} \small 1.0$

Correct answer:

$\dpi{100} \small 6.4$

Explanation:

The distance between points $\dpi{100} \small A$ and $\dpi{100} \small B$ is 6.4. Point $\dpi{100} \small A$ is at $\dpi{100} \small (-2,-3)$ . Point $\dpi{100} \small B$ is at $\dpi{100} \small (2,2)$ . Putting these points into the distance formula, we have $\sqrt{(-2-2)^{2}+(-3-2)^{2}}=\sqrt{(-4)^{2}+(-5)^{2}}=\sqrt{16+25}=\sqrt{41}\approx 6.4$ .

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Example Question #2 : How To Find The Length Of A Line With Distance Formula

What is the slope of the line between points $\dpi{100} \small A$ and $\dpi{100} \small B$ ?

Possible Answers:

$\frac{5}{4}$

$5$

$\frac{-5}{4}$

$\frac{5}{2}$

$-4$

Correct answer:

$\frac{5}{4}$

Explanation:

The slope of the line between points $\dpi{100} \small A$ and $\dpi{100} \small B$ is $\frac{5}{4}$ . Point $\dpi{100} \small A$ is at $\dpi{100} \small (-2,-3)$ . Point $\dpi{100} \small B$ is at $\dpi{100} \small (2,2)$ . Putting these points into the slope formula, we have $\frac{-3-2}{-2-2}=\frac{-5}{-4}=\frac{5}{4}$ .

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Example Question #744 : Act Math

What is the distance between $\left ( 1,-2 \right )$ and $\left ( 6,10 \right )$ ?

Possible Answers:

Correct answer:

Explanation:

Let $P_{1}=(1,-2)$ and $P_{2}=(6,10)$ and use the distance formula: $d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$ . The distance formula is a specific application of the more general Pythagorean Theorem: $a^{2} + b^{2} = c^{2}$ .

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Example Question #745 : Act Math

What is the distance, in coordinate units, between the points $(-2,6)$ and $(5,-2)$ in the standard $(x,y)$ coordinate plane?

Possible Answers:

$\sqrt{7}$

$15$

$\sqrt{15}$

$\sqrt{113}$

$113$

Correct answer:

$\sqrt{113}$

Explanation:

The distance formula is $\sqrt{((x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2})}=d$ , where $d$ = distance.

Plugging in our values, we get

$d=\sqrt{((5-(-2))^{2}+(6-(-2))^{2}}=\sqrt{7^{2}+8^{2}}=\sqrt{49+64}=\sqrt{113}$

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ACT Math : ACT Math

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

Example Question #2 : How To Find The Equation Of A Line

Example Question #3 : How To Find The Equation Of A Line

Example Question #4 : How To Find The Equation Of A Line

Example Question #741 : Act Math

Example Question #742 : Act Math

Example Question #743 : Act Math

Example Question #2 : How To Find The Length Of A Line With Distance Formula

Example Question #744 : Act Math

Example Question #745 : Act Math

All ACT Math Resources

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