Question

Write y - 2 = ⅖(x + 2) in slope-intercept form.

Answer 1

To write the equation \( y - 2 = \frac{2}{5}(x + 2) \) in slope-intercept form, we need to solve for \( y \).

1. Start with the original equation:
\[
y - 2 = \frac{2}{5}(x + 2)
\]

2. Distribute \( \frac{2}{5} \) on the right side:
\[
y - 2 = \frac{2}{5}x + \frac{2}{5} \cdot 2
\]
\[
y - 2 = \frac{2}{5}x + \frac{4}{5}
\]

3. Now, add 2 to both sides to isolate \( y \):
\[
y = \frac{2}{5}x + \frac{4}{5} + 2
\]

4. Convert the 2 to a fraction with a denominator of 5:
\[
2 = \frac{10}{5}
\]

5. Add the fractions on the right side:
\[
y = \frac{2}{5}x + \frac{4}{5} + \frac{10}{5}
\]
\[
y = \frac{2}{5}x + \frac{14}{5}
\]

Thus, the equation in slope-intercept form \( y = mx + b \) is:
\[
y = \frac{2}{5}x + \frac{14}{5}
\]

Here, the slope \( m \) is \( \frac{2}{5} \) and the y-intercept \( b \) is \( \frac{14}{5} \).