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A scatterplot graph shows x-axis ranging from 0 to 100 and y-axis ranging from 0 to 50. Both axes are drawn in increments of 5 but labeled in increments of 10. Multiple points are plotted around a line that points upward to the right.
The line passes through left parenthesis 0 comma 30 right parenthesis, left parenthesis 15 comma 40 right parenthesis, and left parenthesis 30 comma 50 right parenthesis. 14 points are plotted close to or on the line. The line has an arrowhead on the top of it.

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

(1 point)
Responses

y = 2/3x + 40

y = 2/3x + 30

y = 3/4x + 30

y = −2/3 x +30

1 answer

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

From the points given in the description:

  • One point is (0, 30), which indicates that the y-intercept (b) is 30.
  • Two other points provided are (15, 40) and (30, 50).

Now we can determine the slope (m) using these two points:

  1. Calculate the slope (m) using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points (15, 40) and (30, 50): \[ m = \frac{50 - 40}{30 - 15} = \frac{10}{15} = \frac{2}{3} \]

With the slope \( m = \frac{2}{3} \) and the y-intercept \( b = 30 \), we can write the equation of the trend line as: \[ y = \frac{2}{3}x + 30 \]

Therefore, the correct response is: y = 2/3x + 30.