Ask a New Question
Menu

Use the image to answer the question.

An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 30 in increments of 2. Multiple points are plotted around a line that points upward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 12 right parenthesis, left parenthesis 4 comma 16 right parenthesis, and left parenthesis 6 comma 18 right parenthesis. 12 points are plotted close to the line.

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

(1 point)
y=
+

1 answer

To write the equation in slope-intercept form (y = mx + b) of the trend line given the points it passes through, we first determine the slope (m) and the y-intercept (b).

  1. Calculate the slope (m) using two points on the line. We can use the points (0, 12) and (4, 16).

    The formula for calculating the slope is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

    Plugging in the values: \[ m = \frac{16 - 12}{4 - 0} = \frac{4}{4} = 1 \]

  2. Determine the y-intercept (b). Since the line passes through the point (0, 12), we can see that when x = 0, y = 12. Therefore, the y-intercept b = 12.

  3. Write the equation in slope-intercept form: Substituting the values of m and b into the equation: \[ y = 1x + 12 \] or simply: \[ y = x + 12 \]

Thus, the equation of the trend line is: \[ y = x + 12 \]