Question

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

Answer 1

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

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

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

Using the points (3, 0) \((x_1, y_1)\) and (0, -2) \((x_2, y_2)\):

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

Now that we have the slope \(m = \frac{2}{3}\), we can use one of the points to find the y-intercept \(b\). We will use the point (0, -2), where \(x = 0\) and \(y = -2\).

In the slope-intercept form, when \(x = 0\), \(b\) is the y-coordinate:

\[
b = -2
\]

Now we have both \(m\) and \(b\). We can write the equation of the line:

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

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

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