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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+30
y equals negative 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=34x+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 provided.

From the points provided, we can calculate the slope (m) using the formula:

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

Let's first take two points from the line: (15, 40) and (30, 50).

Using those points:

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

Now, we have the slope (m) as \(\frac{2}{3}\).

Next, we use one of the points to find the y-intercept (b). We can use the point (15, 40):

\[ y = mx + b \] \[ 40 = \frac{2}{3}(15) + b \] \[ 40 = 10 + b \] \[ b = 40 - 10 = 30 \]

Now we can write the equation of the trend line in slope-intercept form:

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

Among the answer choices provided, the correct equation is:

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