Question

use the scatter plot and the trend line to show answer a-c. Write an equation for the trend line. predict the value of y when x =21 Predict the value of x when y = 150

Answer 1

Answer:

See Explanation

Step-by-step explanation:

This question is incomplete, as the required scatter plot is not included in the question. I will answer your question with the attached plot.

Solving (a): The equation

Pick any $two$  $points$on the $trend$ line

$(x_1,y_1) = (30,40)$

$(x_2,y_2) = (80,70)$

$y = 0.6x + 22$

Calculate the slope (m)

$m = \frac{y_2 - y_1}{x_2 -x_1}$

$m = \frac{70 - 40}{80-30}$

$m = \frac{30}{50}$

$m = 0.6$

The equation is then calculated as:

$y = m(x - x_1) + y_1$

This gives:

$y = 0.6(x - 30) + 40$

$y = 0.6x - 18 + 40$

$y = 0.6x + 22$

Solving (b): y, when $x = 21$

$y = 0.6x + 22$

Substitute $x = 21$

$y = 0.6 * 21 + 22$

$y = 12.6 + 22$

$y = 34.6$

Solving (c): x when $y=150$

$y = 0.6x + 22$

Substitute $y=150$

$150 = 0.6x + 22$

Collect like terms

$0.6x = 150 -22$

$0.6x = 128$

Solve for x

$x = \frac{128}{0.6}$

$x = 213.3$