Question

What is the of the line in slope- intercept from. (0,-2) (3,0)

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) and the y-intercept (b) using the given points (0, -2) and (3, 0).

1. **Calculate the slope (m)** using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Let (x1, y1) = (0, -2) and (x2, y2) = (3, 0). Then:
\[
m = \frac{0 - (-2)}{3 - 0} = \frac{0 + 2}{3} = \frac{2}{3}
\]

2. **Identify the y-intercept (b)**: Since one of the points is (0, -2), we know that the y-intercept, b, is -2.

3. **Write the equation in slope-intercept form**:
\[
y = mx + b
\]
Substituting in the values for m and b, we get:
\[
y = \frac{2}{3}x - 2
\]

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