Question

Bivariate Data Analysis & Probability Unit Test
5 of 165 of 16 Items











Question
Use the image to answer the question.

An illustration of a scatterplot graph shows x-axis ranging from 0 to 15 in increments of 1 and y-axis ranging from 0 to 75 in increments of 5. Multiple points are plotted and a line points upward to the right with an arrowhead on the top.
The line passes approximately through left parenthesis 0 comma 25 right parenthesis, left parenthesis 1 comma 30 right parenthesis, left parenthesis 2 comma 35 right parenthesis, left parenthesis 7 comma 60 right parenthesis, and left parenthesis 10 comma 75 right parenthesis. 5 points are plotted to the line.

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

(1 point)
y=
x +

Answer 1

To find 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:
- Point 1: (0, 25)
- Point 2: (1, 30)
- Point 3: (2, 35)
- Point 4: (7, 60)
- Point 5: (10, 75)

**Step 1: Calculate the slope (m)**
The slope \(m\) can be calculated using any two points. Let's use points (1, 30) and (2, 35):

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{35 - 30}{2 - 1} = \frac{5}{1} = 5
\]

**Step 2: Use one point to find the y-intercept (b)**
We can use point (0, 25) to find \(b\). Using the slope-intercept form:

\[
y = mx + b \\
25 = 5(0) + b \\
b = 25
\]

**Final Equation**
Now that we have \(m\) and \(b\), we can write the equation of the trend line:

\[
y = 5x + 25
\]

So, in slope-intercept form, the equation is:

\[
y = 5x + 25
\]