Use the image to answer the question.

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)
y=
x-
Remaining Attempts : 3

Answer 1

To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).

1. Identify two points on the line: From the description, we have the points (0, -2) and (3, 0).

2. Calculate the slope (m): The formula for slope is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (0, -2) and (3, 0):

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

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

3. Use one point to find the y-intercept (b): We can use the y-intercept point (0, -2). When \(x = 0\), \(y = -2\), thus \(b = -2\).

4. Write the equation: Now that we have the slope and y-intercept, we can write the equation:

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

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

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