Write an equation of the line that passes through (1,2) and is parallel to the line y=-5x+4

Answer 1

In order to write in equation of a line in the form of y=mx+b, we need as much of the following as possible:

m = a slope

b = a y-intercept

(x,y) = a point that lies upon the line

We have most of this. In order to be parallel, two lines must have the exact same slope. We know the known line that the unknown line is parallel to had a slope of -5. We have a point that lies upon the line: (1,2). If we plug this in, we only need to find the intercept.

2 = -5(1) + b. Multiply -5 and 1

2 = -5 + b. Add 5 to both sides of the equal sign

7 = b.

The intercept is known. Finally, write the equation for any point that could be on the line. Leave x and y as variables:

y = -5x + 7

Answer 2

Parallel lines have equal slopes, so

y = -5x + b

Use the given point to find b.

2 = -5(1) + b

You can finish from here.