Equation of a line parallel

Question

What is the equation of a line parallel to y=4/5x +2 that passes through (1,2)?

Answer 1

parallel lines have the same slope

slope = the coefficient of the x term when the equation is solved for y

slope = 4/5

slope also = the difference in y coordinates divided by the difference in x coordiates

slope = (y-2)/(x-1)

set those two values for the slope equal

(y-2)/(x-1) = 4/5

y-2 = (4/5)(x-1) in point slope form

y-2 = 4x/5 - 4/5

y = 4x/5 -4/5 +2

y = 4x/5 -4/5 + 10/5

y = 4x/5 +6/5 in slope intercept form

5y=4x +6

4x-5y+6 = 0 in standard linear form

Answer 2

I. For a parallel line, the slope of the two lines must be the same.

The slope (m) is 4/5.

II. Point slope form of the linear line: y-y₀=m(x-x₀)

(x₀,y₀) is a point on the line. In this case, this is given to you as (1,2)

III. Plug in (x₀,y₀) and m

y-y₀=m(x-x₀)

y-2=(4/5)(x-1)