Use the image to answer the question.

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

y=1x+9
y
=
1
x
+
9
y equals 1 x plus 9

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

y=−14x

Answer 1

To determine the correct equation of the trend line in slope-intercept form (y = mx + b), we need to first identify the slope (m) and the y-intercept (b) of the line.

Looking at the points given:

• (0, 9)
• (4, 8)
• (8, 7)
• (10, 6.5)

We can find the slope (m) using two of the points. Let's use the points (0, 9) and (4, 8):

The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting the points into the formula: \[ m = \frac{8 - 9}{4 - 0} = \frac{-1}{4} \]

So the slope \( m = -\frac{1}{4} \).

Now, we can use the y-intercept from the point (0, 9), which indicates that \( b = 9 \).

Thus, the equation of the trend line is: \[ y = -\frac{1}{4}x + 9 \]

Looking at the provided responses, the corresponding option is: y = −14x + 9 (this seems to be a typo; it should be y = -1/4x + 9).

The correct equation to choose from the given options is: y = −1/4 x + 9.