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.

Question

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+30
y equals 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+40
y equals Start Fraction 2 over 3 End Fraction x plus 40

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, we can select two points to calculate the slope:

Let's use the points (15, 40) and (30, 50).

1. Calculate the slope (m):

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

2. Now that we have the slope, we can use one of the points to find the y-intercept (b). Using the point (15, 40):

\[ y = mx + b \implies 40 = \frac{2}{3}(15) + b \]

Calculating:

\[ 40 = 10 + b \implies b = 40 - 10 = 30 \]

3. Now we can write the equation in slope-intercept form:

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

Thus, the correct response is:

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