Question

(a) find the slope of the line through (7,2) and (48, -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. (a) select the correct choice below and, if necessary, fill in the answer box to complete your choice. a. the slope of the line is (type an integer or a simplified fraction) b. the slope is undefined.

Explanation:

Part (a)

Step1: Recall the slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).
Here, \( (x_1, y_1)=(7, 2) \) and \( (x_2, y_2)=(48, - 2) \).

Step2: Substitute the values into the formula

Substitute \( x_1 = 7 \), \( y_1 = 2 \), \( x_2 = 48 \), and \( y_2=-2 \) into the slope formula:
\( m=\frac{-2 - 2}{48 - 7}=\frac{-4}{41} \)

A line with a negative slope falls from left to right, a positive slope rises from left to right, a slope of \( 0 \) is horizontal, and an undefined slope is vertical. Since the slope we found in part (a) is \( -\frac{4}{41} \) (which is negative), the line falls from left to right.

Answer:

A. The slope of the line is \(\boldsymbol{-\frac{4}{41}}\)

Part (b)