Question

The two graphs below compare the gallons of gasoline used and the total distance traveled for two different cars. Car 1 A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 50) and (4, 100). Car 2 A graph has gallons of gasoline used on the x-axis and miles traveled on the y-axis. A line goes through points (2, 40) and (4, 80). Which comparison of the slopes of the two lines is accurate?

Answer 1

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Answer:

slope of Car 1’s graph is 5 greater than the slope of Car 2’s graph.

Step-by-step explanation:

$\mathfrak{ to \:compare\:the\:slopes}$

$\mathfrak{ formulae \:used}$-$slope=y$₂$-y$₁ /$x$₂-

From the first graph, the line passes through the points (2, 50) and (4, 100), thus the slope of the first graph is given by:

$slope=y$₂$-y$₁ /$x$₂-

$=100-50/4-2\\=50/2\\=25$

From the second graph, the line passes through the points (2, 40) and (4, 80), thus the slope of the second graph is given by:

$slope=y$₂$-y$₁ /$x$₂-

$=80 -40/4-2\\=40/2\\=20$

Therefore, the slope of Car 1’s graph is 5 greater than the slope of Car 2’s graph.

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Answer 2

$\mathfrak{dear\:user }$

$\mathfrak{ here\:is\:your\:answer }$-$\textsf{the slope of Car 1’s graph is 5 greater than the slope of Car 2’s graph.}$

$\mathfrak{ to \:compare\:the\:slopes}$

$\mathfrak{ formulae \:used}$-$slope=y$₂$-y$₁ /$x$₂-$x$₁

From the first graph, the line passes through the points (2, 50) and (4, 100), thus the slope of the first graph is given by:

$slope=y$₂$-y$₁ /$x$₂-$x$₁

$=100-50/4-2\\=50/2\\=25$

From the second graph, the line passes through the points (2, 40) and (4, 80), thus the slope of the second graph is given by:

$slope=y$₂$-y$₁ /$x$₂-$x$₁

$=80 -40/4-2\\=40/2\\=20$

Therefore, $\textsf{the slope of Car 1’s graph is 5 greater than the slope of Car 2’s graph.}$

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