Question

Use the two points (4,92) and (1,82) from the scatterplot and the slope formula to find the slope of a linear model (regression line), rounded to three decimal places. Show your work. (5 points)
Using the slope and a point from question (a) to write the equation of the linear model in point-slope form? (5 points)

Simplify the equation you wrote in problem (b) into slope-intercept form. Show your work. (5 points)

Answer 1

Answer:

a) The slope is : 3.333

b) $(y-92)=3.333(x-4)$

c) $y=3.333x+78.66$

Step-by-step explanation:

a) - The formula to calculate the slope is:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

- Use the given points to calculate the slope:

$y_{2}=82\\y_{1}=92\\x_{2}=1\\x_{1}=4$

$m=\frac{82-92}{1-4}\\m=\frac{10}{3}\\m=3.333$

b) - The equation of the linear model in point-slope form is:

$(y-y_{1})=m(x-x_{1})$

Where $m$ is the slope and $x_{1},y_{1}$ are the coordinates of a point.

- Substitute values:

$(y-92)=3.333(x-4)$

c) - The equation of the linear model in slope-intercept form is:

$y=mx+b$

Where $m$ is the slope and $b$ is the y-intercept.

- Let's find $b$. Use one of the points given in the problem to solve for $b$:

$92=3.333(4)+b\\b=92-13.332\\b=78.66$

- Therefore, the equation is:

$y=3.333x+78.66$