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PSAT Math : How to find slope of a line

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Example Questions

Example Question #1 :Slope And Line Equations

Based on the table below, when x = 5, y will equal

x	y
-1	3
0	1
1	-1
2	-3

Possible Answers:

–9

–10

–11

Correct answer:

–9

Explanation:

使用图2点找到方程of the line.

Example: (–1, 3) and (1, –1)

Using the formula for the slope, we find the slope to be –2. Putting that into our equation for a line we get y = –2x + b. Plug in one of the points for x and y into this equation in order to find b. b = 1.

The equation then will be: y = –2x + 1.

Plug in 5 for x in order to find y.

y = –2(5) + 1

y = –9

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Example Question #2 :Slope And Line Equations

What is the slope of a line that runs through points: (-2, 5) and (1, 7)?

Possible Answers:

2/3

3/2

5/7

Correct answer:

2/3

Explanation:

The slope of a line is defined as a change in the y coordinates over a change in the x coordinates (rise over run).

To calculate the slope of a line, use the following formula:

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Example Question #3 :Slope And Line Equations

A line passes through the points (–3, 5) and (2, 3). What is the slope of this line?

Possible Answers:

–2/3

2/5

2/3

-3/5

–2/5

Correct answer:

–2/5

Explanation:

The slope of the line that passes these two points are simply ∆y/∆x = (3-5)/(2+3) = -2/5

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Example Question #4 :Slope And Line Equations

Which of the following lines intersects they-axis at a thirty degree angle?

Possible Answers:

y=x

y=x√2 - 2

y=x√3 + 2

y=x((√3)/3) + 1

y=x- √2

Correct answer:

y=x√3 + 2

Explanation:

Line_intersect1

Line_intersect2

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Example Question #5 :Slope And Line Equations

What is a possible slope of liney?

Possible Answers:

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small -\frac{1}{2}$

–2

Correct answer:

–2

Explanation:

The slope is negative as it starts in quadrant 2 and ends in quadrant 4. Slope is equivlent to the change inydivided by the change inx. The change inyis greater than the change inx, which implies that the slope must be less than –1, leaving –2 as the only possible solution.

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Example Question #6 :Slope And Line Equations

What is the slope between (8,3) and (5,7) ?

Possible Answers:

$-\frac{5}{2}$

$\frac{2}{5}$

$-\frac{4}{3}$

$\frac{3}{4}$

$\frac{1}{6}$

Correct answer:

$-\frac{4}{3}$

Explanation:

Let $P_{1}=(8,3)$ and $P_{2}=(5,7)$

$m = (y_{2} - y_{1}) \div (x_{2} - x_{1})$ so the slope becomes $-\frac{4}{3}$ .

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Example Question #7 :Slope And Line Equations

$\textup{What is the slope of a line perpendicular to the line with the equation}$

$3y+2x=6\textup{ ?}$

Possible Answers:

$\frac{-2}{3}$

$\frac{-3}{2}$

$\textup{Connot be determined with this information.}$

$\frac{2}{3}$

$\frac{3}{2}$

Correct answer:

$\frac{3}{2}$

Explanation:

$\textup{Get into }y=mx+b\textup{ format: }3y=-2x+6\:,\:y=-\frac{2}{3}x+2$

$\textup{Perpendicular slope is negative reciprocal of }-\frac{2}{3}\: \rightarrow \rightarrow \frac{3}{2}$

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Example Question #8 :Slope And Line Equations

Axes

Refer to above red line. What is its slope?

Possible Answers:

$-\frac{1}{3}$

$\frac{1}{3}$

Correct answer:

Explanation:

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-6, y_{1}=x_{2}= 0, y_{2}=18$ :

$m = \frac{18-0}{0-(-6)} = \frac{18}{3} = 3$

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Example Question #9 :Slope And Line Equations

Which of the following equations has as its graph a line with slope 4?

Possible Answers:

4y = x + 7

4x+y = 7

None of the other responses is correct.

4y + x = 7

4x= y + 7

Correct answer:

4x= y + 7

Explanation:

For each equation, solve forand express in the slope-intercept form y=mx + b . The coefficient ofwill be the slope.

4x+y = 7

4x+y- 4x = 7 - 4x

y = -4x + 7

Slope: m = -4

4y + x = 7

4y + x- x = 7 - x

4y = -x + 7

$\frac{4y}{4} =\frac{ -x + 7}{4}$

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

Slope: $m = - \frac{1}{4}$

4y = x + 7

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

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

Slope: $m = \frac{1}{4}$

4x= y + 7

4x- 7= y + 7 - 7

y = 4x - 7

Slope: m = 4 .

The line of the equation

4x= y + 7

is the one with slope 4.

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PSAT Math : How to find slope of a line

Study concepts, example questions & explanations for PSAT Math

All PSAT Math Resources

Example Questions

Example Question #1 :Slope And Line Equations

Example Question #2 :Slope And Line Equations

Example Question #3 :Slope And Line Equations

Example Question #4 :Slope And Line Equations

Example Question #5 :Slope And Line Equations

Example Question #6 :Slope And Line Equations

Example Question #7 :Slope And Line Equations

Example Question #8 :Slope And Line Equations

Example Question #9 :Slope And Line Equations

All PSAT Math Resources

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