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Graphing Equations Practice

Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
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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)

1 answer

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. Find the slope (m): The slope can be calculated using the formula:

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

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

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

  2. Find the y-intercept (b): The y-intercept is the value of y when x = 0. From the point (0, -2), we can see that:

    \[ b = -2 \]

  3. Write the equation: Now we can substitute m and b into the slope-intercept form:

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

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

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