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)

Question

Responses/

y=x−1
y equals x minus 1

y=−x−2
y equals negative x minus 2

y=−x+3
y equals negative x plus 3

y=−x−5

Answer 1

To find the equation of a line in slope-intercept form (y = mx + b) that passes through the point (−5, 3) and has a slope of −1, we can follow these steps:

1. Identify the slope (m): Given as −1.
2. Use the point (−5, 3): Here, x = −5 and y = 3.
3. Plug the values into the slope-intercept equation:

Starting with the general form: \[ y = mx + b \]

Substituting the slope: \[ y = -1x + b \] or \[ y = -x + b \]

Now, use the point (−5, 3) to find b (the y-intercept): \[ 3 = -(-5) + b \] \[ 3 = 5 + b \]

Now, solve for b: \[ b = 3 - 5 \] \[ b = -2 \]

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).