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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) of the line.

From the points mentioned, we can select two points to calculate the slope:

Let’s choose the points (0, 25) and (10, 75).

Calculating the slope (m):

The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Using the points (0, 25) and (10, 75):

\[ m = \frac{75 - 25}{10 - 0} = \frac{50}{10} = 5 \]

Finding the y-intercept (b):

The y-intercept (b) can be found by substituting one of the points into the slope-intercept equation (y = mx + b). We can use the point (0, 25):

\[ 25 = 5(0) + b \]

This simplifies to:

\[ b = 25 \]

Now, substituting the values of m and b into the slope-intercept form equation:

\[ y = 5x + 25 \]

Thus, the equation of the trend line is:

\[ y = 5x + 25 \]