Write an equation of the line in standard form for these two?

Question

1. parallel to y= -2x+6 through (-8,5)

2. perpendicularr to y=3x+1 , through (-9,2)

Answer 1

The first one is y = -2x + b and you solve for b by plugging in the (-9,2) point fo rthe x and y values, So
2 = -2*(-9) + b and b = -16 so the final equation is
y = - 2x - 16.

A perpendicular line has a slope that is the negative reciprocal of the first line. Since the given line has a slope of 3, the perpendicular has slope of -1/3 and it's equation is y = (-1/3)*x + b. Find the value of b just like above. 2 = (-1/3)*(-9) + b => b = -1 so final equation is
y = (-1/3)*x - 1


Doug

Answer 2

1. parallel lines have the same slope. the slope of the given equation is -2. The line that has the slope -2 and that passes through the point (-8,5) is the following (point-slope form):
y - 2 = -2(x + 8)
converting to standard form:
y - 2 = -2x = 8
2x - y = 10

2. The slopes of perpendicular lines are the negative reciprocals of each other. The slope of the given equation is 3. The slope of any line that is perpendicular to this given equation is -1/3. to find the equation with slope -1/3 that passes through (-9,2), use the point slope form:
y - 2 = -1/3(x + 9)
multiply through by 3 to clear the equation of fractions:
3y - 6 = -(x + 9)
3y - 6 = -x -9
x + 3y = -3

Answer 3

1)
"Parallel" = same slope
The slope of the given line is -2 (it's in front of the x).
So you know the slope of the line (m) and a point on the line (x1,y1). Write it in point-slope form:
(y - y1) = m(x - x1)
(y - 5) = -2(x + 8)
y - 5 = -2x - 16
You can know put this in standard form:
Ax + By = C
y + 2x = -11

2)
"Perpendicular" = negative of the reciprocal of the slope
The slope of your given line is 3. Therefore the slope of a perpendicular line is -1/3.
Do the same thing as in part (1):
(y - 2) = (-1/3)*(x + 9)
y - 2 = -(1/3)x - 3
y + (1/3)x = -1

Answer 4

1. Two lines are parallel iff their slopes are equal. In this case the slope is -2. Plug this in with the given point into the point-slope formula to get:
y-y1=m(x-x1)
y-5=-2(x+8)
y=-2x-16+5
y=-2x-11

2. Two lines are perpendicular iff their slopes are both the additive and multiplicative of each other. In this case the slope is 3 so the perpendicular slope is -1/3. Plug this in like before to get:
y-y1=m(x-x1)
y-2=(-1/3)(x+9)
The rest is up to you!

Answer 5

1.parallel to y=-2x+6
so the equation is y=2x+k
passes through (-8,5)
plugging in 5=16+k
k=-11
so the equation is y=-2x-11
=>2x+y+11=0

2.perpendicular to y=3x+1
so the equation is -3y=x+k
passes through(-9,2)
plugging in -6=-9+k
k=3
the equation is -3y=x+3
=>x+3y+3=0