Question

What is the equation in slope-intercept form of the line that passes through the point (-6, 3) and
has a slope of 5/3?

Answer 1

To find the equation of a line in slope-intercept form (which is \( y = mx + b \)), we need the slope \( m \) and the y-intercept \( b \).

We are given:
- A point \((-6, 3)\)
- A slope \( m = \frac{5}{3} \)

Using the slope-intercept form, we can first substitute the slope and the coordinates of the given point into the point-slope formula, which is:

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

Substituting \( m = \frac{5}{3} \), \( x_1 = -6 \), and \( y_1 = 3 \):

\[
y - 3 = \frac{5}{3}(x + 6)
\]

Now, we simplify the equation. First, distribute the slope on the right side:

\[
y - 3 = \frac{5}{3}x + \frac{5}{3} \cdot 6
\]

Calculating \( \frac{5}{3} \cdot 6 \):

\[
\frac{5 \cdot 6}{3} = \frac{30}{3} = 10
\]

So, we have:

\[
y - 3 = \frac{5}{3}x + 10
\]

Next, add 3 to both sides to isolate \( y \):

\[
y = \frac{5}{3}x + 10 + 3
\]
\[
y = \frac{5}{3}x + 13
\]

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

\[
\boxed{y = \frac{5}{3}x + 13}
\]