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=−2/3x+30
y equals negative Start Fraction 2 over 3 End Fraction x plus 30

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

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

y=3/4x+30

Answer 1

To determine the equation in slope-intercept form (y = mx + b) of the trend line from the provided points on the scatterplot, we first need to find the slope (m) and the y-intercept (b) of the line.

1. Identify Points on the Line: The line passes through the points (0, 30), (15, 40), and (30, 50).

2. Calculate the Slope (m): The slope can be calculated using any two points on the line. Using points (0, 30) and (15, 40): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{40 - 30}{15 - 0} = \frac{10}{15} = \frac{2}{3} \]

3. Determine the Y-Intercept (b): The y-intercept can be found directly from the first point (0, 30). Here, when x = 0, y = 30. This means: \[ b = 30 \]

4. Write the Equation: Now that we have the slope and y-intercept, we can write the equation: \[ y = \frac{2}{3}x + 30 \]

Based on the options given, the correct response is:

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