In the xy-plane, a line passes through the points (2, 9) and (5, 21). What is the slope of… — SAT

In the $xy$ -plane, a line passes through the points $(2, 9)$ and $(5, 21)$ . What is the slope of this line?

Answer: 4

The slope of the line is 4.

The slope

m

of a line passing through the points

(x_1, y_1)

and

(x_2, y_2)

is determined by the formula

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

. Substituting the given points

(2, 9)

and

(5, 21)

into the formula gives

m = \frac{21 - 9}{5 - 2} = \frac{12}{3} = 4

Identify the coordinates of the two points on the line.

(x_1, y_1) = (2, 9)

and

(x_2, y_2) = (5, 21)

These points are used in the slope formula.

Apply the slope formula

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

to set up the calculation.

m = \frac{21 - 9}{5 - 2}

The slope is defined as the change in

y

divided by the change in

x

Simplify the fraction to calculate the final slope.

m = \frac{12}{3} = 4

Dividing the vertical change by the horizontal change yields the slope.

Calculating the slope of a line given two points in the coordinate plane.

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