A line in the standard (x, y) coordinate plane passes through the points (3, -2) and (7, 6… — ACT

A line in the standard $(x, y)$ coordinate plane passes through the points $(3, -2)$ and $(7, 6)$ . What is the slope of this line?

Answer: 2

The slope of the line is

2

The correct answer is

2

. The slope of a line passing through

(x_1, y_1)

and

(x_2, y_2)

is given by the formula

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

. Substituting

(3, -2)

and

(7, 6)

gives

m = \frac{6 - (-2)}{7 - 3} = \frac{8}{4} = 2

Identify the coordinates of the two points on the line.

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

and

(x_2, y_2) = (7, 6)

The coordinates are needed to apply the slope formula.

Apply the slope formula

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

m = \frac{6 - (-2)}{7 - 3}

The slope is the ratio of the vertical change (rise) to the horizontal change (run).

Simplify the numerator and the denominator, then divide.

m = \frac{8}{4} = 2

Subtracting a negative value is equivalent to addition, which yields the final slope of

2

Slope formula

Question