A line with a slope of $ \frac{1}{5} $ passes through the points (2, -5) and (a, -6). What is the value...

Question

A line with a slope of $ \frac{1}{5} $ passes through the points (2, -5) and (a, -6). What is the value of a?

SnapAndSolve AI · Accepted Answer

To find the value of a, use the slope formula:

\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Given slope = $ \frac{1}{5} $, $ (x_1, y_1) = (2, -5) $, $ (x_2, y_2) = (a, -6) $.

\[ \frac{-6 - (-5)}{a - 2} = \frac{1}{5} \]

\[ \frac{-1}{a - 2} = \frac{1}{5} \]

Cross-multiply to solve for a:

\[ -1 \times 5 = 1 \times (a - 2) \]

\[ -5 = a - 2 \]

\[ a = -5 + 2 \]

\[ a = -3 \]

The value of a is -3.

A line with a slope of \( \frac{1}{5} \) passes through the points (2, -5) and (a, -6). What is the value...