Question

Give that the slope of a line is 2/3
and a point on that line is (-1,3), what is the equation for that line in Slope Intercept Form?

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 given slope and the point on the line.

Given:
- Slope \( m = \frac{2}{3} \)
- Point \( (-1, 3) \) where \( x = -1 \) and \( y = 3 \)

1. **Plug the point and slope into the point-slope formula**:
\[
y - y_1 = m(x - x_1)
\]
Substituting \( m = \frac{2}{3} \), \( x_1 = -1 \), and \( y_1 = 3 \):
\[
y - 3 = \frac{2}{3}(x + 1)
\]

2. **Distribute the slope**:
\[
y - 3 = \frac{2}{3}x + \frac{2}{3}
\]

3. **Add 3 to both sides to solve for \( y \)**:
\[
y = \frac{2}{3}x + \frac{2}{3} + 3
\]

Convert 3 to a fraction with a denominator of 3:
\[
3 = \frac{9}{3}
\]

Now combine the fractions:
\[
y = \frac{2}{3}x + \frac{2}{3} + \frac{9}{3}
\]
\[
y = \frac{2}{3}x + \frac{11}{3}
\]

Thus, the equation of the line in slope-intercept form is:
\[
y = \frac{2}{3}x + \frac{11}{3}
\]