Questions: (a) Find the slope of the line through (-5,1) and (7,-3). (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.

$(a) Find the slope of the line through (-5,1) and (7,-3). (b) Based on the slope, indicate whether the line through the points rises from left to right, falls from left to right, is horizontal, or is vertical. (a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of the line is (Type an integer or a simplified fraction.) B. The slope is undefined.$

Transcript text: (a) Find the slope of the line through $(-5,1)$ and $(7,-3)$. (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 $\square$ (Type an integer or a simplified fraction.) B. The slope is undefined.

Solution

Solution Steps

Step 1: Calculate the slope of the line

The slope $m$ of the line is calculated using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given values, $m = \frac{-3 - 1}{7 + 5} = -0.33$.

Step 2: Determine the orientation of the line

The line falls from left to right, which means its slope is negative.