Question

Tamara is analyzing a line that passes through the point (−5,3) and has a slope of −1 . How should she write the equation of the line in slope-intercept form?(1 point) Responses y=x−1 y equals x minus 1 y=−x−5 y equals negative x minus 5 y=−x+3 y equals negative x plus 3 y=−x−2

Answer 1

To write the equation of a line in slope-intercept form \( y = mx + b \), you need the slope \(m\) and the y-intercept \(b\).

Given:
- Point: \((-5, 3)\)
- Slope: \(-1\)

1. Start with the slope-intercept form:
\[ y = mx + b \]
Substitute the slope \(m = -1\):
\[ y = -x + b \]

2. Now, use the point \((-5, 3)\) to find \(b\):
Substitute \(x = -5\) and \(y = 3\):
\[ 3 = -(-5) + b \]
\[ 3 = 5 + b \]
Solving for \(b\):
\[ b = 3 - 5 \]
\[ b = -2 \]

3. Now, substitute back to get the equation of the line:
\[ y = -x - 2 \]

So the correct response is:
\[ y = -x - 2 \]