Versions of Linear Equations Quick Check

Question

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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−5
y equals negative x minus 5

y=−x−2
y equals negative x minus 2

y=−x+3
y equals negative x plus 3

y=x−1

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we can use the point-slope form of the line equation:

1. The slope (m) is given as -1.
2. The line passes through the point (−5, 3).

Using the point-slope form:

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

We can plug in the values:

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

Now, simplify this equation:

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

2. Add 3 to both sides to solve for y: \[ y = -x - 5 + 3 \] \[ y = -x - 2 \]

Therefore, the equation of the line in slope-intercept form is:

y = -x - 2

So the correct response is:

y = -x - 2 (y equals negative x minus 2).