SSAT Upper Level Quantitative - How to find slope of a line

What is the slope of a line which passes through coordinates $\dpi{100} \small (3,7)$ and $\dpi{100} \small (4,12)$ ?

$\dpi{100} \small 5$

$\dpi{100} \small \frac{1}{5}$

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

$\dpi{100} \small 2$

$\dpi{100} \small 3$

Explanation

Slope is found by dividing the difference in the $\dpi{100} \small y$ -coordinates by the difference in the $\dpi{100} \small x$ -coordinates.

$\dpi{100} \small \frac{(12-7)}{(4-3)}=\frac{5}{1}=5$

Find the slope of the line that goes through the points $(7, 15)\text{ and }(-3, -12)$

$\frac{27}{10}$

$\frac{10}{27}$

$-\frac{10}{27}$

$-\frac{27}{10}$

Explanation

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Plug in the given points to find the slope.

$\text{Slope}=\frac{-12-15}{-3-7}=\frac{-27}{-10}=\frac{27}{10}$

What is the slope of a line that passes though the coordinates $(5,2)$ and $(3,1)$ ?

$\frac{1}{2}$

$-\frac{1}{2}$

$-\frac{2}{3}$

$\frac{2}{3}$

$4$

Explanation

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

$m=\frac{y_2-y_1}{x_2-x_1}$

Use the give points in this formula to calculate the slope.

$m=\frac{1-2}{3-5}=\frac{-1}{-2}=\frac{1}{2}$

What is the slope of a line that passes through the points $(15, -2)\text{ and }(-16, 20)$ ?

$-\frac{22}{31}$

$\frac{22}{31}$

$-\frac{31}{22}$

$\frac{31}{22}$

Explanation

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Plug in the given points to find the slope.

$Slope=\frac{20-(-2)}{-16-15}=-\frac{22}{31}$

A line goes passes through the points $\left(-\frac{1}{2}, 5\right)\text{ and }\left(\frac{3}{2}, -1\right)$ . What is the slope of this line?

$-\frac{1}{2}$

$\frac{1}{2}$

Explanation

Use the following formula to find the slope of a line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

The slope of this line would be

$\frac{-1-5}{\frac{3}{2}-(-\frac{1}{2})}=\frac{-6}{2}=-3$

What is the slope of a line running through points and ?

$-\frac{1}{7}$

$\frac{7}{3}$

Explanation

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

$m=\frac{y_2-y_1}{x_2-x_1}$

Use the give points in this formula to calculate the slope.

$m=\frac{3-(-4)}{7-8}=\frac{7}{-1}=-7$

Find the slope of the line that passes through the points $\left(\frac{1}{3}, -\frac{4}{5}\right)$ and $\left ( -6,10\right )$ .

$-\frac{162}{95}$

$\frac{162}{95}$

$-\frac{95}{162}$

$\frac{95}{162}$

Explanation

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Plug in the given points to find the slope.

$\text{Slope}=\frac{10-(-\frac{4}{5})}{-6-\frac{1}{3}}=\frac{\frac{54}{5}}{-\frac{19}{3}}=-\frac{162}{95}$

A line is given with the equation . What is the slope of this line?

Explanation

To find the slope, put the equation in form.

Since , that must be the slope of the line.

A line has the equation . What is the slope of the line?

$\frac{8}{7}$

$-\frac{8}{7}$

$\frac{7}{8}$

$-\frac{7}{8}$

Explanation

Change the equation into the more familiar form. The value of will be the slope.

$y=\frac{8}{7}x-2$

One end of a board that is four feet long is on the ground. The other end is balanced on a box that is one foot tall, creating a slope. What is the slope of the board?

$\frac{1}{4}$

$1\frac{1}{4}$

Explanation

The slope of a line is equal to $\frac{rise}{run}$ .

Given that the box is one foot tall, the rise will be equal to "1."

Given that the board is four feet long, the run will be equal to "4."

Therefore, the slope is equal to $\frac{rise}{run}=\frac{1}{4}$ .

How to find slope of a line

Help Questions

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation

Explanation