|
Question 975075: Write an equation in slope intercept form.
Line contains the point (-3,5) and is perpendicular to the line y=3x-4?
Line contains the point(2,3) and is parallel to 5x-y=10?
Found 2 solutions by lwsshak3, farohw:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write an equation in slope intercept form.
Line contains the point (-3,5) and is perpendicular to the line y=3x-4?
Line contains the point(2,3) and is parallel to 5x-y=10?
***
y=3x-4
slope, m=3
slope of perpendicular line=-1/3 (negative reciprocal)
equation: y=-x/3+b
solve for b using coordinates(-3, 5) on the perpendicular line
b=y-x/3=5-(-3/3)=5+1=6
equation: y=-x/3+6
..
5x-y=10
y=5x-10
slope, m=5
slope of parallel line=5 (same as that of given line )
equation: y=5x+b
solve for b using coordinates(2, 3) on the parallel line
b=y-5x=3-10=-7
equation: y=5x-7
Answer by farohw(175)  (Show Source):
You can put this solution on YOUR website!
As you know, the slope-intercept form is y = mx + b where m = slope and b is the y-intercept.
(a) Line contains the point (-3,5) and is perpendicular to the line y=3x-4
For the equation y = 3x - 4 our slope is perpendicular to the line so we will write m = -1/3 which is the inverse of 3. Next we apply the point-slope formula using our slope, m = -1/3 and points (x1, y1) or (-3,5):
y - y1 = m(x - x1)
y - (5) = -1/3(x - (-3))
y - 5 = -1/3(x + 3)
y - 5 = (-1/3)x - 1 --> y = (-1/3)x - 1 + 5
y = -(1/3)x + 4 and this is your equation in slope-intercept form.
Perpendicular: 
(b) Line contains the point(2,3) and is parallel to 5x-y=10.
We have to put 5x -y = 10 in slope-intercept form first:
-y = -5x + 10 --> dividing the equation by (-1) we change the signs to y = 5x - 10
Your slope is m = 5. Since parallel lines have identical slopes, the parallel line through point (2,3) will have slope m = 5.
Use the point-slope form in (a) to find the line using your slope m = 5 and point (2, 3).
y - y1 = m(x - x1) --> y - 3 = 5(x - 2)
Solving,
y - 3 = 5x - 10
Parallel: y = 5x - 7
|
|
|
| |
