Question

The point-slope form of a line that has a slope of –2 and passes through point (5, –2) is shown below.

y + 2 = negative 2 (x minus 5)

What is the equation in slope-intercept form?
y = negative 2 x + 12
y = negative 2 x + 8
y = negative 2 x minus 7
y = negative 2 x minus 3

Answer 1

To convert the point-slope form of the equation \( y + 2 = -2(x - 5) \) into slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept, we can follow these steps:

1. Start with the point-slope form:
\[
y + 2 = -2(x - 5)
\]

2. Distribute the slope on the right side:
\[
y + 2 = -2x + 10
\]

3. Subtract 2 from both sides to isolate \( y \):
\[
y = -2x + 10 - 2
\]
\[
y = -2x + 8
\]

Thus, the equation in slope-intercept form is:
\[
y = -2x + 8
\]

So the correct option is:
y = negative 2 x + 8.