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Answered

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2.) The information in the table below shows the
distance a car traveled during a number of hours.
Hours (h)
Miles (m)
1
45
2
90
3
135
4
180
Write an equation using the variables h and m that
represents the information in the table

2 The Information In The Table Below Shows The Distance A Car Traveled During A Number Of Hours Hours H Miles M 1 45 2 90 3 135 4 180 Write An Equation Using Th class=

Sagot :

semsee45

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]

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