Use the image to answer the question.

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

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

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

y=−23x+30

Answer 1

To find 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 given.

From the stated points that the line passes through:

1. (0, 30)
2. (15, 40)
3. (30, 50)

First, let's calculate the slope (m) between two of the points. We'll use the points (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 that we have the slope, we can use one of the points to find the y-intercept (b). We can use the point (0, 30):

Since x = 0, by substituting into the equation:

\[ y = mx + b \implies 30 = \frac{2}{3}(0) + b \implies b = 30 \]

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

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

So the correct response is:

y = \(\frac{2}{3}\)x + 30.