GRE Quantitative Reasoning - How to find the 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.

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

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 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.

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

Refer to the following graph:

Gre1

What is the slope of the line shown?

1/3

–1/3

–1

–3

Explanation

One can use either the slope formula m = (y2 – y1)/(x2 – x1) or the standard line equation, y = mx + b to solve for the slope, m. By calculation or observation, one can determine that the slope is –3.

If 2x – 4y = 10, what is the slope of the line?

–5/2

–0.5

0.5

–2

Explanation

First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.

What is the slope of the equation ?

$\frac{1}{2}$

$-\frac{1}{2}$

Explanation

To find the slope of a line, you should convert an equation to the slope-intercept form. In this case, the equation would be $y=\frac{1}{2}x+2$ , which means the slope is $\frac{1}{2}$ .

What is the slope of the line with equation 4_x_ – 16_y_ = 24?

1/4

1/8

–1/4

–1/8

1/2

Explanation

The equation of a line is:

y = mx + b, where m is the slope

4_x_ – 16_y_ = 24

–16_y_ = –4_x_ + 24

y = (–4_x_)/(–16) + 24/(–16)

y = (1/4)x – 1.5

Slope = 1/4

What is the slope of a line passing through the point , if it is defined by:

$\frac{-11}{12}$

$\frac{11}{12}$

$\frac{12}{7}$

$\frac{-7}{12}$

$\frac{-1}{7}$

Explanation

Since the equation is defined as it is, you know the y-intercept is . This is the point . To find the slope of the line, you merely need to use the two points that you have and find the equation:

$\frac{rise}{run}=\frac{-4-7}{12-0}=\frac{-11}{12}$

What is the slope of the line represented by the equation $6y-16x=7$ ?

$\frac{8}{3}$

$\frac{7}{6}$

$16$

$6$

$-16$

Explanation

To rearrange the equation into a $y=mx+b$ format, you want to isolate the $y$ so that it is the sole variable, without a coefficient, on one side of the equation.

First, add $11x$ to both sides to get $6y=7+16x$ .

Then, divide both sides by 6 to get $y=\frac{7+16x}{6}$ .

If you divide each part of the numerator by 6, you get $y=\frac{7}{6}+\frac{16x}{6}$ . This is in a $y=b+mx$ form, and the $m$ is equal to $\frac{16}{6}$ , which is reduced down to $\frac{8}{3}$ for the correct answer.