A line passes through the points (-3, 2) and (5, -4) in a coordinate plane. What is the sl… — ACT

A line passes through the points $(-3, 2)$ and $(5, -4)$ in a coordinate plane. What is the slope of this line?

-\frac{3}{4}

The correct answer shows a slope of

-\frac{3}{4}

. Applying the slope formula

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

to the points

(-3, 2)

and

(5, -4)

yields

\frac{-4 - 2}{5 - (-3)} = \frac{-6}{8}

, which simplifies to

-\frac{3}{4}

Identify the coordinates of the two points and state the slope formula.

The points are

(x_1, y_1) = (-3, 2)

and

(x_2, y_2) = (5, -4)

. The slope formula is

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

To find the slope of a line, we calculate the ratio of vertical change (rise) to horizontal change (run).

Substitute the coordinate values into the slope formula.

m = \frac{-4 - 2}{5 - (-3)}

This sets up the subtraction of the

y

-coordinates in the numerator and the

x

-coordinates in the denominator.

Simplify the numerator and denominator to calculate the final slope.

m = \frac{-6}{8} = -\frac{3}{4}

Subtracting a negative number in the denominator is equivalent to addition:

5 - (-3) = 8

. Simplifying the fraction yields the slope of

-\frac{3}{4}

The slope

m

of a line passing through points

(x_1, y_1)

and

(x_2, y_2)

is defined as the change in

y

divided by the change in

x

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

Question