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

Question

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:

$$\text{C: }-5$$