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)

Answer 1

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

Based on the points identified:

1. Point 1: (15, 40)
2. Point 2: (30, 60)

Step 1: Calculate the slope (m)

The formula for the slope \(m\) is given by:

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

Using our points:

• \( (x_1, y_1) = (15, 40) \)
• \( (x_2, y_2) = (30, 60) \)

Now substituting the values:

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

Step 2: Use the slope and a point to find the y-intercept (b)

Using the slope-intercept form \(y = mx + b\) and substituting one of our points, let's use (15, 40):

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

Step 3: Write the equation

Now, substituting \(m\) and \(b\) into the slope-intercept equation:

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

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

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