Question

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid upward line with arrows on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.

Write the equation of the line in slope-intercept form.

(1 point)

Answer 1

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

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

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

Using the points \((0, -2)\) and \((3, 0)\):

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

Now, plug the values into the slope formula:

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

Now that we have the slope \(m = \frac{2}{3}\), we can use one of the points (either one will work, but we will use \((0, -2)\) since it makes finding \(b\) simpler) to find the y-intercept \(b\).

The y-intercept \(b\) is the \(y\)-value when \(x = 0\), which is given as \(-2\). Therefore, \(b = -2\).

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

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

So, the equation of the line is:

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