Question

Which of the following equations represents a line that is parallel to y=5x-4 and passes through the point, (3,4)?

Answer 1

Slope of given line = 5

Slope of parallel lines is the same, so slope of the line parallel to the given line will be m = 5

We have the slope and a point, using the point-slope form we can write the equation of the line:

y - 4 =5 (x - 3)

y = 5x - 15 + 4

y = 5x - 11

So, the above equation is the desired answer.

Answer 2

The given equation is of the form y=mx+c where m is the slope of line.
Comparing given equation with y=mx+c we get m=5

Parallel lines have equal slopes.
Therefore, slope of required line = m = 5

This required line passes through points (3,4)(x₁,y₁)
Therefore, by slope-point form,

y-y₁=m(x-x₁) 
y-4=5(x-3)
y-4=5x-15
y=5x-11

This the equation of required line