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
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
y equals 1 x plus 9

y=−14x+9

Answer 1

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

From the illustration description:
- The points that the line passes approximately through are:
- (0, 9)
- (4, 8)
- (8, 7)
- (10, 6.5)

1. **Calculating the slope (m):**
The slope (m) can be calculated using two of the points. Let's use (0, 9) and (4, 8):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 9}{4 - 0} = \frac{-1}{4} = -\frac{1}{4}
\]

2. **Finding the y-intercept (b):**
The y-intercept occurs where x = 0. From the point (0, 9), we see that:
\[
b = 9
\]

3. **Writing the equation:**
Now we can substitute the slope and y-intercept into the slope-intercept form equation:
\[
y = -\frac{1}{4}x + 9
\]

Now, let's look at the available response options:
- y = −14x
- y = −\frac{1}{4} x
- y = −\frac{5}{8} x + 9
- y = 1x + 9
- y = −14x + 9

None of these directly matches our equation **(y = −\frac{1}{4} x + 9)**. However, looking at the options more closely, the one that matches our slope is:

**y = −\frac{1}{4} x + 9** (the option is not explicitly among the choices, but based on the calculations above). If we strictly follow the correct answer based on the choices, the nearest identical representation of our work would have been placed under "y equals negative Start Fraction 1 over 4 End Fraction x plus 9".

So the best response to select from the options given is:

**y = −\frac{1}{4} x + 9**