Two streets are parallel on a map, 7th street and 8th street. The map is put on a coordinate plane and the equation for 7th street is 𝑦 = 2𝑥 − 6. 8th street goes through the coordinates (1,3) on the map. Write an equation of the line 8th street is on.(1 point)

Question

Two streets are parallel on a map, 7th street and 8th street. The map is put on a coordinate plane and the equation for 7th street is 𝑦 = 2𝑥 − 6. 8th street goes through the coordinates (1,3) on the map. Write an equation of the line 8th street is on.(1 point)
Responses

8th Street is on y=−12x+72
  8th Street is on y is equal to negative 1 half x plus 7 halves

8th Street is on y=2x+3
  8th Street is on y is equal to 2 x plus 3

8th Street is on y=2x+1
8th Street is on y is equal to 2 x plus 1

8th Street is on y=−12x+1

GPT-4o mini · Answer

Since 7th street has the equation $ y = 2x - 6 $, and 8th street is parallel to 7th street, it will have the same slope. The slope of 7th street is $ 2 $. The equation for 8th street will be in the form $ y = mx + b $, where $ m $ is the slope. Thus, the equation for 8th street will be $ y = 2x + b $. To find the value of $ b $, we can use the point (1, 3) which lies on 8th street. Substituting $ x = 1 $ and $ y = 3 $ into the equation: $$ 3 = 2(1) + b $$ $$ 3 = 2 + b $$ $$ b = 3 - 2 $$ $$ b = 1 $$ Thus, the equation of 8th street is: $$ y = 2x + 1 $$ Therefore, the correct response is: **8th Street is on $ y = 2x + 1 $**.