Slope intercept equation??

Question

Write a slope-intercept equation for a line passing through the given point that is parallel to the given line

(-5, 0), y = -0.9x + 4.1

A.
Parallel: y=0.9x - 4.9
Perpendicular: y= -10/9x - 50 / 9

B.
Parallel: y= -0.9x + 4.5
Perpendicular: y= 10/9x - 50/9

C.
Parallel: y=-0.9x - 4.5
Perpendicular: y= 10/9x + 50/9

Answer 1

The slope of the given line is m = -0.9 (it's the number in front of x).
Parallel means the slopes are equal, so you can go ahead and eliminate choice A because -0.9 does not equal 0.9
Perpendicular lines have the property that the product of the slopes is -1. Both B and C fit this.
Now we need to check the point.
For B
(-5,0), so x = -5 and y = 0
y = mx + b
0 = -0.9(-5) + b
0 = 4.5 + b
-4.5 = b, so the equation is
y = -0.9x + 4.5
Choice C
You can double check that this is your answer by verifying the perpendicular line.
Replace x with -5 and y with 0.
0 = (10/9)(-5) + 50/9
0 = -50/9 + 50/9
0 = 0

Answer 2

The answer is C:

slope of a parallel line is the same slope
slope of a perpendicular line is the negative inverse slope

therefore: parallel line slope: -9/10
AND perpendicular line slope: +10/9

the y intercepts can be calculated by using a proportion:

the y intercept of the parallel line:
set up an upside down right triangle with base divided into two parts. the overall length is 10 and the partition should be at 0 if looking at the coordinate plane. the long negative part of the triangle will have length of -9. so that (-9/10) = (b/5) setting up the vertical length divided by the horizontal length for the whole trangle and then the intercepting triangle.
you will get b=-4.5. In slope intercept for y=-0.9x - 4.5

if you do the same thing for the perpendicular triangle, you will get (10/9) = (y/5) or b=+50/9, therefore in slope intercept form y= 10/9x + 50/9

Answer 3

(-5,0), y=-9/10+41/10

The perpendicular is 10/9

(y-y1)=m(x-x1)
y-0=10/9(x+5)
y=10/9x+50/9

Parallel:
y-0=-9/10(x+5)
y=-9/10x-4.5
y=-0.9x-4.5

The answer is C.