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: \[ y = -x - 2 \]