Question

Tamra 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 (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), Tamra can follow these steps:

1. **Identify the slope and the point**: The slope (\(m\)) is given as -1, and the point is (-5, 3).

2. **Use the point-slope form of the line**: The point-slope form of a linear equation is:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is the point on the line. Here, \((x_1, y_1) = (-5, 3)\), and \(m = -1\).

3. **Substitute the values into the point-slope form**:
\[
y - 3 = -1(x + 5)
\]

4. **Distribute and simplify**:
\[
y - 3 = -1x - 5
\]
\[
y - 3 = -x - 5
\]

5. **Add 3 to both sides** to isolate \(y\):
\[
y = -x - 5 + 3
\]
\[
y = -x - 2
\]

Thus, the equation of the line in slope-intercept form is:
\[
\boxed{y = -x - 2}
\]