SOLUTION: 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?

Algebra.Com
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












RELATED QUESTIONS

Write an equation in slope intercept form for the line described: contains point (4,... (answered by LinnW)
A line contains the point ( - 3, - 4) and is perpendicular to a line with a slope of... (answered by josgarithmetic)
A line contains the point (-3, -4) and is perpendicular to a line with a slope of 3/5.... (answered by josgarithmetic)
A line contains the point ( - 6, 7) and has a slope of . Write an equation of the line... (answered by ikleyn)
A line contains the point ( - 6, 7) and has a slope of . Write an equation of the line... (answered by ikleyn,greenestamps,josgarithmetic)
A line contains the point ( - 3, - 4) and is perpendicular to a line with a slope of... (answered by josgarithmetic)
can you write an equation in slope-intercept form for the lie that contains the given... (answered by jim_thompson5910)
write in slope-intercept form the equation of the line that passes through the given... (answered by mananth)
Write an equation of a line that is perpendicular to the line y=(2/3)x + 5 and contains... (answered by richwmiller)