(-2,1); y = -4x + 3

Question

write an equation of the line that passes through the given point and is parallel to the given line? please help

Answer 1

Dear Jacqueline,

Please do me the courtesy of reading my entire answer rather than just harvesting the solution to the problem.

Point (-2,1)

Line: y = -4x + 3

The given point is not on the line given. Rather, it is on many other lines, including a line that is parallel to the given line. We are asked to find the equation to that parallel line that has the given point on it. That means that when the x- and y-coordinates are filled into the parallel line's equation, the mathematical statement is true.

The KEY fact is that parallel lines have the SAME SLOPE. Thus, we need to find the slope of the given line so that we can give this slope to our parallel line that we are "creating."

Since the given line (y = -4x + 3) already is written in point-slope form, we can read off the slope directly. It is the coefficient of the x-term: –4.

Thus, the template of our parallel line can be filled in with the slope.

Template: y = mx + b

y = –4x + b

We only need to determine what the value of b is. We do this by filling in the x-coordinate and y-coordinate of the given point into the equation.

Point (-2,1) <x,y>

y = –4x + b

1 = (–4)(–2) + b

1 = 8 + b

–7 = b

So now we go back to our partially finished equation for the parallel line and fill in the value of b that we calculated.

y = –4x – 7

This is the equation of the line that contains the given point and is parallel to the given line.

Answer 2

y = mx+b is slope intercept form of equation of line, so for y = -4x + 3 , slope is -4.

Line parallel to that line will have the same slope = -4

so equation of that line is y = -4x + b

We need to find b. Since we know that line passes through (-2,1) substitute -2 for x and 1 for y to find b:

1 = -4(-2) + b

b = -7

y = -4x -7