Question

Use the points (60, 0) and (85,30) to find the slope of the equation.

y =
x - 72

Based on the trend line, what is the expected value of y when x = 90? (Use the trend line, not the equation)

The expected value of y is

Answer 1

To find the slope of the line defined by the points \( (60, 0) \) and \( (85, 30) \), we can use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging in our points:

- \( (x_1, y_1) = (60, 0) \)
- \( (x_2, y_2) = (85, 30) \)

We get:

\[
m = \frac{30 - 0}{85 - 60} = \frac{30}{25} = \frac{6}{5} = 1.2
\]

So the slope of the trend line is \( 1.2 \).

Now, to find the expected value of \( y \) when \( x = 90 \) using the trend line, we first need to find the y-intercept of the line. Since we have a slope \( m = 1.2 \) and one point \( (60, 0) \), we can use the point-slope form of the line:

\[
y - y_1 = m(x - x_1)
\]

Using point \( (60, 0) \):

\[
y - 0 = 1.2(x - 60)
\]

Simplifying:

\[
y = 1.2x - 1.2 \times 60
\]
\[
y = 1.2x - 72
\]

Now we can use this equation to find the expected value of \( y \) when \( x = 90 \):

\[
y = 1.2(90) - 72
\]
\[
y = 108 - 72
\]
\[
y = 36
\]

Thus, the expected value of \( y \) when \( x = 90 \) is:

\[
\text{The expected value of } y \text{ is } 36.
\]