Question

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Trend Lines Quick Check
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Question
Use the image to answer the question.

A scatterplot graph shows x-axis ranging from 0 to 100 and y-axis ranging from 0 to 50. Both axes are drawn in increments of 5 but labeled in increments of 10. Multiple points are plotted around a line that points upward to the right.
The line passes through left parenthesis 0 comma 30 right parenthesis, left parenthesis 15 comma 40 right parenthesis, and left parenthesis 30 comma 50 right parenthesis. 14 points are plotted close to or on the line. The line has an arrowhead on the top of it.

Write an equation in slope-intercept form of the trend line.

(1 point)
Responses

y=34x+30
y equals Start Fraction 3 over 4 End Fraction x plus 30

y=23x+30
y equals Start Fraction 2 over 3 End Fraction x plus 30

y=23x+40
y equals Start Fraction 2 over 3 End Fraction x plus 40

y=−23x+30
y equals negative Start Fraction 2 over 3 End Fraction x plus 30
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Answer 1

To write 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 points described:
- The line passes through the points (0, 30), (15, 40), and (30, 50).

Using the points to calculate the slope \(m\):

We can use two points to find the slope. Let's use (15, 40) and (30, 50):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{50 - 40}{30 - 15} = \frac{10}{15} = \frac{2}{3}
\]

Now, we know that the slope \(m = \frac{2}{3}\).

Next, we will use the y-intercept, which is the value of \(b\) when \(x = 0\). From the point (0, 30), we can see that the y-intercept \(b = 30\).

Putting the values into the slope-intercept form \(y = mx + b\), we get:

\[
y = \frac{2}{3}x + 30
\]

So, the correct response is:
**y = \(\frac{2}{3}\)x + 30**.

This corresponds to: **y equals Start Fraction 2 over 3 End Fraction x plus 30**.