PSAT Math : How to find slope of a line

Study concepts, example questions & explanations for PSAT Math

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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:

–11

–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

 

 

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:

2/3

5/7

3/2

2

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: Actmath_7_113_q7

 

 

Example Question #1 : 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

-3/5

–2/5

–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

Example Question #1 : Geometry

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

Possible Answers:

y = x√2 - 2

y = x

y = x - √2

yx((√3)/3) + 1

y = x√3 + 2

Correct answer:

y = x√3 + 2

Explanation:

Line_intersect1

Line_intersect2

Example Question #1 : Geometry

What is a possible slope of line y?

Possible Answers:

–2

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

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.

Example Question #1 : Geometry

What is the slope between  and ?

Possible Answers:

Correct answer:

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 .

Example Question #1 : Slope And Line Equations

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Geometry

Axes

Refer to above red line. What is its slope?

Possible Answers:

Correct answer:

Explanation:

The slope of a line. given two points  can be calculated using the slope formula

Set :

Example Question #1 : Geometry

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

Possible Answers:

None of the other responses is correct.

Correct answer:

Explanation:

For each equation, solve for  and express in the slope-intercept form . The coefficient of  will be the slope.

 

Slope: 

 

Slope: 

 

 

Slope: 

 

 

Slope: 

 

The line of the equation 

is the one with slope 4.

 

 

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