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An illustration of a scatterplot graph is titled Animal Longevity. It shows x-axis, labeled as average, ranging from 0 to 45 in increments of 5 and y-axis, labeled as maximum, ranging from 0 to 80 in increments of 10.
Multiple points are plotted around a line that points upward to the right with an arrowhead on the top. The line passes approximately through left parenthesis 0 comma 20 right parenthesis, left parenthesis 15 comma 40 right parenthesis, left parenthesis 30 comma 60 right parenthesis, and left parenthesis 40 comma 78 right parenthesis. Two dotted lines are drawn forming a triangle under the line with the line being the hypotenuse. The dotted lines are drawn from left parenthesis 15 comma 40 right parenthesis to left parenthesis 30 comma 40 right parenthesis and from left parenthesis 30 comma 60 right parenthesis to left parenthesis 30 comma 40 right parenthesis. 8 points are plotted close to the line.

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

(1 point)
y=
x +

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 (\(b\)) based on the points provided.

  1. Identify two points on the trend line to calculate the slope. We can use the points \((15, 40)\) and \((30, 60)\).

    \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{60 - 40}{30 - 15} = \frac{20}{15} = \frac{4}{3} \]

  2. Now that we have the slope \(m = \frac{4}{3}\), we can use one of the points to find the y-intercept \(b\). Let's use the point \((15, 40)\).

    \[ y = mx + b \] \[ 40 = \frac{4}{3}(15) + b \] \[ 40 = 20 + b \] \[ b = 40 - 20 = 20 \]

  3. Now we can write the equation in slope-intercept form:

    \[ y = \frac{4}{3}x + 20 \]

Thus, the final answer is:

\[ y = \frac{4}{3}x + 20 \]