Question

What is the slope of the line given by the equation y- 10 = -5 ( x + 20)?

A: -20

B: 10

C: -5

D: 5

Answer 1

To find the slope of the line given by the equation \( y - 10 = -5 ( x + 20) \), we can either rewrite the equation in slope-intercept form \( y = mx + b \), where \( m \) is the slope, or we can directly identify the slope from the equation.

Starting with the given equation:

\[
y - 10 = -5 (x + 20)
\]

First, distribute the -5 on the right-hand side:

\[
y - 10 = -5x - 100
\]

Next, add 10 to both sides to isolate \( y \):

\[
y = -5x - 100 + 10
\]

This simplifies to:

\[
y = -5x - 90
\]

Now, the equation is in slope-intercept form \( y = mx + b \), where \( m \) is the slope. Here, the slope \( m = -5 \).

Thus, the slope of the line is:

\[
\text{C: } -5
\]