Question

points: (3,0) (0,-2)
Write the equation of the line in slope-intercept form.

Answer 1

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

The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting in the points:

- \((x_1, y_1) = (3, 0)\)
- \((x_2, y_2) = (0, -2)\)

We have:

\[
m = \frac{-2 - 0}{0 - 3} = \frac{-2}{-3} = \frac{2}{3}
\]

Now that we have the slope \(m = \frac{2}{3}\), we can use one of the points to find the y-intercept \(b\).

Let's use the point \((0, -2)\) (where \(x = 0\), so this point gives us the y-intercept directly):

Since when \(x = 0\), \(y = -2\), we have:

\[
b = -2
\]

Now we can write the equation of the line in slope-intercept form:

\[
y = \frac{2}{3}x - 2
\]

Thus, the equation of the line is:

\[
y = \frac{2}{3}x - 2
\]