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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 +
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Answer 1

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

From the points provided, we can identify two points to calculate the slope:

• Point 1: \( (0, 25) \)
• Point 2: \( (10, 75) \)

Using the formula for the slope \(m\): \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the coordinates of the two points: \[ m = \frac{75 - 25}{10 - 0} = \frac{50}{10} = 5 \]

Now, we have the slope \(m = 5\). To find the y-intercept \(b\), we can use one of the points, for example, \( (0, 25) \): \[ y = mx + b \] Substituting \(x = 0\) and \(y = 25\): \[ 25 = 5(0) + b \implies b = 25 \]

Now we have both \(m\) and \(b\): \[ y = 5x + 25 \]

So, the equation of the trend line in slope-intercept form is: \[ \boxed{y = 5x + 25} \]