What is the equation of a line passing through (5,2) and parallel to the line represented by the equation y = 2x + 1?

y = 2x - 8

Step-by-step explanation:

To find the equation of a line passing through (5,2) and parallel to the line represented by the equation y = 2x + 1, we will follow the steps below;

since the line is parallel to y=2x + 1, then the will have the same slope. That is; m₁ = m₂

comparing y = 2x + 1 to y = mx + c

m = 2

we will substitute m = 2 x = 5 and y = 2 into y = mx + c and then solve for c

y = mx + c

2 = 2 (5) + c

2 = 10 + c

subtract 10 from both-side of the equation

2-10 = 10 - 10 + c

-8 = c

c=-8

To find our equation, we will substitute m = 2 and c=-8 into y=mx + c

y = 2x - 8

Therefore, the equation of a line passing through (5,2) and parallel to the line represented by the equation y = 2x + 1 is y = 2x - 8