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−2
y equals negative x minus 2

y=−x+3
y equals negative x plus 3

y=−x−5
y equals negative x minus 5

y=x−1

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we can use the given point (−5, 3) and the slope m = −1.

1. Start with the slope-intercept form:
\( y = mx + b \)

2. Substitute the slope for m:
\( y = -x + b \)

3. Now, use the point (−5, 3) to find b. Substitute x = −5 and y = 3 into the equation:
\( 3 = -(-5) + b \)
\( 3 = 5 + b \)

4. Solve for b:
\( b = 3 - 5 \)
\( b = -2 \)

5. Now we can write the equation of the line:
\( y = -x - 2 \)

Therefore, the correct response is:
**y = −x − 2** (y equals negative x minus 2).