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+3
y equals negative x plus 3

y=x−1
y equals x minus 1

y=−x−2
y equals negative x minus 2

y=−x−5

Answer 1

To find the equation of the 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 line equation, which is given by:

\[ y - y_1 = m(x - x_1) \]

where \( (x_1, y_1) \) is a point on the line, and \( m \) is the slope.

Given that the point is \( (-5, 3) \) and the slope \( m \) is \( -1 \), we can substitute these values into the point-slope form:

\[ y - 3 = -1(x + 5) \]

Now, we can simplify this equation step-by-step:

1. Distribute the slope on the right side:

\[ y - 3 = -x - 5 \]

2. Add 3 to both sides to isolate \( y \):

\[ y = -x - 2 \]

Now we have the equation of the line in slope-intercept form. Therefore, the correct response is:

\[ y = -x - 2 \]

So, the answer is: y = −x − 2.