Use the image to answer the question.

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=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

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

y=23x+30

Answer 1

Bot GPT 4-o mini answered
8 days ago

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) based on the points given.

From the points you provided:

(0, 30) is the y-intercept, so b = 30.
The slope (m) can be calculated using the formula: \[ m = \frac{\Delta y}{\Delta x} \]

We can use two of the points to calculate the slope. Let's use the points (0, 30) and (30, 50):

\(\Delta y = 50 - 30 = 20\)
\(\Delta x = 30 - 0 = 30\)

Now, calculate the slope:

\[ m = \frac{20}{30} = \frac{2}{3} \]

Now that we have both the slope and the y-intercept:

m = \(\frac{2}{3}\)
b = 30

Thus, the equation of the trend line is:

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

This gives us the answer:

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