Line ℓ can be represented by the equation y=53x.

Line m is shown on this graph.

Select the statement that correctly explains which line has a greater slope and why.

Line ℓ has a greater slope because 53 is greater than 13.Line ell has a greater slope because 5 thirds is greater than

Line m has a greater slope because 13 is greater than 53.Line m has a greater slope because 1 third is greater than

Line ℓ has a greater slope because 53 is greater than 31.Line ell has a greater slope because 5 thirds is greater than

Line m has a greater slope because 31 is greater than 53.

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joaobezerra joaobezerra · Answer 1 · 2022-06-24T18:32:18+02:00

Using linear function concepts, the correct statement is given by:

Line l has a greater slope, because [tex]\frac{5}{3}[/tex] is greater than [tex]\frac{1}{3}[/tex].

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

Line l is given by:

[tex]y = \frac{5}{3}x[/tex].

For line m, considering that the slope is given by change in y divided by change in x, the slope is:

[tex]m = \frac{2 - 0}{3 - (-3)} = \frac{1}[3}[/tex]

Hence, the correct statement is:

Line l has a greater slope, because [tex]\frac{5}{3}[/tex] is greater than [tex]\frac{1}{3}[/tex].

More can be learned about linear function concepts at https://brainly.com/question/24808124

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