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?

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 start with the given slope and a point on the line.

The slope \( m \) is given as \( -1 \), and the point through which the line passes is \( (-5, 3) \).

We can use the point-slope form of the equation of a line, which is given by:

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

Here, \( (x_1, y_1) \) is the point \((-5, 3)\). Substituting the values into the point-slope form:

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

Next, we'll 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 \( y \):

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

3. Combine like terms:

\[
y = -x - 2
\]

Now, we have the equation of the line in slope-intercept form:

\[
\boxed{y = -x - 2}
\]