Tamara is analyzing a line that passes through the point (−5,3)

Question

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+3
y equals negative x plus 3

y=−x−2
y equals negative x minus 2

y=−x−5

Answer 1

To write the equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we can use the point-slope form of the equation and convert it.

Given:

• Point: (−5, 3)
• Slope (m): −1

1. Start with the point-slope form: \[ y - y_1 = m(x - x_1) \] Here, (x_1, y_1) is the point (−5, 3).

2. Plug in the values: \[ y - 3 = -1(x + 5) \]

3. Distribute the slope on the right: \[ y - 3 = -x - 5 \]

4. Solve for y: \[ y = -x - 5 + 3 \] \[ y = -x - 2 \]

So the equation of the line in slope-intercept form is: \[ y = -x - 2 \]

The correct response is: y = −x − 2 (y equals negative x minus 2).