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

a) The slope is : 3.333

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

c)
`y=3.333x+78.66`

Explanation:

a) - The formula to calculate the slope is:

`m=(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=(82-92)/(1-4)\\m=(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`