Use the image to answer the question.

Question

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 +

Answer 1

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 information provided, we can use two points that the line passes through: \((15, 40)\) and \((30, 60)\).

1. Calculate the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{60 - 40}{30 - 15} = \frac{20}{15} = \frac{4}{3} \]

2. Use point-slope form to calculate \(b\) (the y-intercept): We can use one of the points, say \((15, 40)\), and insert the slope: \[ y = mx + b \implies 40 = \frac{4}{3}(15) + b \] Now calculate: \[ 40 = 20 + b \implies b = 40 - 20 = 20 \]

3. Write the equation: Now we can write the equation of the trend line: \[ y = \frac{4}{3}x + 20 \]

Thus, in the required format, the equation of the trend line is: \[ y = \frac{4}{3}x + 20 \]