Question

The first line is dot-dashed and is labeled Line 1. Line 1 passes through coordinates left parenthesis 0 comma 40 right parenthesis and left parenthesis 2 comma 70 right parenthesis. The second line is labeled Line 2 and is solid. Line 2 passes through coordinates left parenthesis 0 comma 10 right parenthesis and left parenthesis 1.5 comma 70 right parenthesis. The third line is labeled Line 3 and is dotted. Line 3 passes through coordinates left parenthesis 0.5 comma 20 right parenthesis and left parenthesis 1 comma 50 right parenthesis. The fourth line is long dot-dashed and is labeled Line 4. Line 4 passes through coordinates left parenthesis 0.5 comma 10 right parenthesis and left parenthesis 2 comma 70 right parenthesis.

Sara went to meet her friend Rianna in Rome, but Rianna left Rome on a train 15 minutes earlier. The distance traveled by the train, in miles, with respect to time can be modeled by the equation y=40x+10
. Sara can buy a ticket on a faster train that will leave in 10 minutes and follow the same route. If the distance of the faster train with respect to time can be modeled by the equation y=60x−10
, which two lines on the graph show the solution to when Sara’s train catches up to Rianna’s train?

(1 point)

Line 3 and Line 4

Line 1 and Line 2

Line 2 and Line 3

Line 1 and Line 4

Answer 1

Line 2 is y = 40x + 10 (slope 40, intercept 10) and Line 3 is y = 60x − 10 (slope 60, intercept −10). Setting them equal: 40x+10 = 60x−10 gives x = 1 (y = 50). So Sara catches up at (1,50). Answer: Line 2 and Line 3.