Question: (a) Find the slope of the line through \((-14, -15)\) and \((-10, 2)\). (b) Based on the…

(a) Find the slope of the line through \((-14, -15)\) and \((-10, 2)\).

(b) Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical.

(b) Choose the correct answer below.

A. The line is horizontal.

B. The line through the points falls from left to right.

C. The line is vertical.

D. The line through the points rises from left to right.

A. The slope is

(Type an integer or a simplified fraction)

B. The slope is undefined.

Solution

To find the slope of the line passing through the points \((-14, -15)\) and \((-10, 21)\), we can use the slope formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1}& \] Substituting the given points: \[ m = \frac{21 - (-15)}{-10 - (-14)}& \] Calculate the numerator and denominator: \[ m = \frac{36}{4}& \] Simplify: \[ m = 9& \] Therefore, the slope of the line is \(9\).