Answer:
m = 45h
Step-by-step explanation:
Calculate the difference in y-values (miles):
[tex]45 \underset{+45}{\longrightarrow} 90\underset{+45}{\longrightarrow} 135\underset{+45}{\longrightarrow} 180[/tex]
As the number of miles increases by the same amount for every increase of an hour, the equation is linear.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given variables:
- x = Hours (h)
- y = Miles (m)
As the number of miles increases by 45 miles for each increase of an hour, the slope of the linear equation is 45:
[tex]\implies m=45h+b[/tex]
To find b, substitute one of the ordered pairs into the equation and solve for b:
[tex]\implies 45=45(1)+b[/tex]
[tex]\implies 45=45+b[/tex]
[tex]\implies b=45-45[/tex]
[tex]\implies b=0[/tex]
Therefore, the equation using the variables h and m that represents the information in the given table is:
[tex]\boxed{m=45h}[/tex]
