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PSAT Math : How to find slope of a line

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Example Questions

Example Question #1 : Geometry

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

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

Possible Answers:

–10

–9

–11

Correct answer:

–9

Explanation:

Use 2 points from the chart to find the equation 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 #1 : Slope And Line Equations

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

Possible Answers:

5/7

3/2

2/3

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 #1 : Psat Mathematics

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

Possible Answers:

–2/5

2/3

2/5

-3/5

–2/3

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 #2 : Geometry

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

Possible Answers:

y = x - √2

y = x

y = x√3 + 2

y = x√2 - 2

y = x((√3)/3) + 1

Correct answer:

y = x√3 + 2

Explanation:

Line_intersect1

Line_intersect2

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Example Question #1 : Psat Mathematics

What is a possible slope of line y?

Possible Answers:

–2

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

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

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 in y divided by the change in x. The change in y is greater than the change in x, which implies that the slope must be less than –1, leaving –2 as the only possible solution.

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Example Question #1 : Lines

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

Possible Answers:

$\frac{1}{6}$

$-\frac{4}{3}$

$\frac{2}{5}$

$-\frac{5}{2}$

$\frac{3}{4}$

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 #1 : How To Find Slope Of A Line

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

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

Possible Answers:

$\frac{-3}{2}$

$\frac{-2}{3}$

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

$\frac{2}{3}$

$\frac{3}{2}$

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 #3 : 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 #1 : Psat Mathematics

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

Possible Answers:

None of the other responses is correct.

4y + x = 7

4y = x + 7

4x= y + 7

4x+y = 7

Correct answer:

4x= y + 7

Explanation:

For each equation, solve for and express in the slope-intercept form y=mx + b . The coefficient of will 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 : Geometry

Example Question #1 : Slope And Line Equations

Example Question #1 : Psat Mathematics

Example Question #2 : Geometry

Example Question #1 : Psat Mathematics

Example Question #1 : Lines

Example Question #1 : How To Find Slope Of A Line

Example Question #3 : Slope And Line Equations

Example Question #1 : Psat Mathematics

All PSAT Math Resources

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