Question

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 30 in increments of 2. Multiple points are plotted around a line that points upward to the right with an arrowhead on the bottom.
The line passes approximately through left parenthesis 0 comma 12 right parenthesis, left parenthesis 4 comma 16 right parenthesis, and left parenthesis 6 comma 18 right parenthesis. 12 points are plotted close to the line.

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

(1 point)
y=
+

Answer 1

To find the equation of the trend line in slope-intercept form (y = mx + b), we start by determining the slope (m) and the y-intercept (b).

From the points mentioned, we can use two points to calculate the slope. For example, we can use (4, 16) and (6, 18).

1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{18 - 16}{6 - 4} = \frac{2}{2} = 1 \]

2. Determine the y-intercept (b): We can use the slope and one of the points to find the y-intercept. Using the point (4, 16): \[ y = mx + b \implies 16 = 1(4) + b \implies 16 = 4 + b \implies b = 16 - 4 = 12 \]

So the equation of the trend line is: \[ y = 1x + 12 \]

In slope-intercept form, this is written as: \[ y = x + 12 \]

Thus, the final answer is:

y = x + 12