Answer:
a) The slope is : 3.333
b) [tex](y-92)=3.333(x-4)[/tex]
c) [tex]y=3.333x+78.66[/tex]
Step-by-step explanation:
a) - The formula to calculate the slope is:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
- Use the given points to calculate the slope:
[tex]y_{2}=82\\y_{1}=92\\x_{2}=1\\x_{1}=4[/tex]
[tex]m=\frac{82-92}{1-4}\\m=\frac{10}{3}\\m=3.333[/tex]
b) - The equation of the linear model in point-slope form is:
[tex](y-y_{1})=m(x-x_{1})[/tex]
Where [tex]m[/tex] is the slope and [tex]x_{1},y_{1}[/tex] are the coordinates of a point.
- Substitute values:
[tex](y-92)=3.333(x-4)[/tex]
c) - The equation of the linear model in slope-intercept form is:
[tex]y=mx+b[/tex]
Where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept.
- Let's find [tex]b[/tex]. Use one of the points given in the problem to solve for [tex]b[/tex]:
[tex]92=3.333(4)+b\\b=92-13.332\\b=78.66[/tex]
- Therefore, the equation is:
[tex]y=3.333x+78.66[/tex]
