Question

What is the equation of the line parallel to the line y=1/4x+5 and passing through the point (2,-1)

Answer 1

The answer is

`y = (1)/(4) x + (1)/(2)`

Explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To find the equation of the parallel line we must first find the slope of the original line

The equation of the line is

y = 1/4x + 5

Comparing with the general equation above

Slope / m = 1/4

Since the lines are parallel their slope are also the same

Slope of parallel line = 1/4

So the equation of the line using point (2,-1) and slope 1/4 is

`y + 1 = (1)/(4) (x - 2) \\ y - 1 = (1)/(4) x - (1)/(2) \\ y = (1)/(4) x - (1)/(2) + 1`

We have the final answer as

`y = (1)/(4) x + (1)/(2)`

Hope this helps you