Use the image to answer the question.

Question

An illustration of a scatterplot graph shows x-axis ranging from 0 to 15 in increments of 1 and y-axis ranging from 0 to 75 in increments of 5. Multiple points are plotted and a line points upward to the right with an arrowhead on the top.
The line passes approximately through left parenthesis 0 comma 25 right parenthesis, left parenthesis 1 comma 30 right parenthesis, left parenthesis 2 comma 35 right parenthesis, left parenthesis 7 comma 60 right parenthesis, and left parenthesis 10 comma 75 right parenthesis. 5 points are plotted 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 first need to determine the slope \(m\) and the y-intercept \(b\) using the points given.

From the points provided, we can calculate the slope \(m\) using two of the points, for example, \((0, 25)\) and \((10, 75)\):

1. Calculate the change in \(y\) (vertical change) and the change in \(x\) (horizontal change): \[ m = \frac{\Delta y}{\Delta x} = \frac{75 - 25}{10 - 0} = \frac{50}{10} = 5 \]

So, the slope \(m\) is 5.

2. Now we use the slope and one of the points to find \(b\). Using the point \((0, 25)\): \[ y = mx + b \implies 25 = 5(0) + b \implies b = 25 \]

Now we can write the equation of the trend line:

\[ y = 5x + 25 \]

So the final answer in slope-intercept form is:

\[ y = 5x + 25 \]