Given an equation of a line, how do I find equations for lines parallel to it going through specified points Simplifying the equations into slope-intercept form.

Question

1. y= -2x -4; (1, 3) how do I write the equation of a line parallel to the given line but passing through the given point
2. y= 3x + 3; (1,1) how do I write the equation of a line perpendicular to the given line but passing through the given point

Answer 1

It must have the same slope: -2
Now you have a point and a slope, so the line is
y-3 = -2(x-1)

same idea, but you want the perpendicular slope, which is the negative reciprocal of the line's slope: -1/3
y-1 = -1/3(x-1)

review the various forms of the equation of a line:

standard
point-slope
two-point
slope-intercept

Answer 2

1. Y = -2x - 4. (1,3).
Parallel lines have equal slopes:
m1 = m2 = -2.

Y = mx + b = 3
-2*1 + b = 3
b = 3+2 = 5
Eq: Y = -2x + 5

2. Y = 3x+3. (1,1).
The slope of the line is equal to the negat1ive reciprocal of the slope of the given line.
m1 = 3
m2 = -1/3.

Y = mx + b = 1
(-1/3)*1 + b = 1
b = 1 + 1/3 = 1 1/3 = 4/3

Eq: Y = (-1/3)x + 4/3