Question

The equation of a line is y=1/4x-2 what is the equation of the line that is parallel to the first line and passes through (4,-2)

Answer 1

To find the equation of this line, we must first find the slope of the line. Since the line is parallel to y = 1/4x - 2, the slope of our line is also 1/4.

So far, we only know the slope, so the equation is y = 1/4x + b. But, we know that this line goes through the point (4, -2), so we can substiute the x and y values and solve.

-2 = 4 (1/4) + b

-2 = 1 + b

b = -3

That means that the equation of this line is y = 1/4x - 3

Answer 2

Since the lines are parallel, they have the same slope.

Slope of first line: y=1/4x-2

Slope of parallel line: y=1/4x+b

Plug in the point that the line passes through to find b. Plug 4 in for x and -2 in for y.

-2=1/4(4)+b

Multiply.

-2=1+b

Subtract 1 from both sides.

-3=b

Equation of the parallel line: y=1/4x-3

Hope this helps! :)