Question

Trend Lines Quick Check
3 of 53 of 5 Items






Question
Use the image to answer the question.

An illustration of a scatterplot graph shows x-axis ranging from 0 to 10 in increments of 1 and y-axis ranging from 0 to 10 in increments of 1. Multiple points are plotted around a line that points downward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 9 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 8 comma 7 right parenthesis, and left parenthesis 10 comma 6.5 right parenthesis. 12 points are plotted close to the line.

Write an equation in slope-intercept form of the trend line.

(1 point)
Responses

y=−14x+9
y equals negative Start Fraction 1 over 4 End Fraction x plus 9

y=−14x
y equals negative Start Fraction 1 over 4 End Fraction x

y=−58x+9
y equals negative Start Fraction 5 over 8 End Fraction x plus 9

y=1x+9

Answer 1

To write 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 you provided, we can estimate the slope using two points on the line. Let's take the points (0, 9) and (4, 8):

1. The change in y (Δy) from (0, 9) to (4, 8) is:
Δy = 8 - 9 = -1

2. The change in x (Δx) from (0, 9) to (4, 8) is:
Δx = 4 - 0 = 4

3. The slope (m) is given by:
m = Δy / Δx = -1 / 4 = -1/4

Now, we can find the y-intercept (b). Since one of the points on the line is (0, 9), we can use it to determine that:

b = 9

Now, we can write the equation of the trend line using the slope and y-intercept:

y = -1/4x + 9

Therefore, the correct response is:

**y equals negative Start Fraction 1 over 4 End Fraction x plus 9**