Jacob walked for x miles and then cyded for y miles between ivs home and the tbrary, the number of mles jacob cydled was 3 mies more than twice the number of miles he walked. the total number of mies cydled was 6 miles which graph best shows the number of wies jacob wallked and cycled?

See the figure attached. The solution is the intersection point (1.5, 6), which means Jacob walked 1.5 mile and cycled 6 miles.

Explanation:

1) Transform the verbal language into algebraic language:

i) Jacob walked for x miles ⇒ variable x


ii) Then cyded for y miles between ⇒ variable y


iii) The number of mles Jacob cydled was 3 miles more than twice the number of miles he walked.

⇒ y = 3 + 2x


iv)The total number of mies cycled was 6 miles ⇒ y = 6


2) To find the solution by the graph method you draw both lines y = 3 + 2x, and  y = 6, in the same coordinate system.

The solution is the intersection point of the two lines.

See the graph attached where the solution is the point (1.5, 6) meaning that Jacob walked 1.5 mile and cycled 6 miles.

3) You can verify the solution algebraically:

      y = 3 + 2x
      y = 6

i) Equal both equations:

      3 + 2x  = 6
⇒ 2x = 3 ⇒ x = 3/2 = 1.5, and y = 6

Which confirms the solution found graphically.