How to write an equation for a line perpendicular to....?

Question

1a) Write a line perpendicular to y=2x-5 that passes through the point (-9,6)

1b)write an equation for the line parallel to y=2x-5 with y intercept 8.

Answer 1

a. ok for a perpendicular line, your slope is the negative reciprocal, so in this case the slope is -1/2, if it passes through the points (-9,6) then use (point slope formula )y-y1=m(x-x1) so then you should plug in your numbers so you would get y-6=-1/2(x+9) then that would be y-6=-1/2x-4.5, add 6 and the final answer should be y=-1/2x+1.5
b. if the line is parallel, the slopes are the same, so in this case 2, if the y intercept is 8 then the point (0,8) must be on the graph so do the same thing as above with the point slope formula. So first your get y-y1=m(x-x1), after plugging it in you should get y-8=2(x-0), then you get y-8=2x, add 8 to each side and get y=2x+8

Answer 2

The slope of the perpendicular line is -1/slope. The slope is the coefficient of x, in case 1a that is 2, so the slope of the perpendicular line is -1/2. The equation for that line is then y = -(1/2)x + b. Find b by putting the point -9,6 into the equation: 6 = -(1/2)*(-9) + b, and solve for b.

The slope of the parallel line is the same as the slope of the original line, in this case that is 2, so the equation of the parallel line is y = 2x + b. The y intercept is the value of y at x = 0, which is b, so b = 8 and the equation is y = 2x + 8,

Answer 3

perpendicular lines have slopes that are negative reciprocals of each other. in this case in (a) the slope of the perpendicular line will thus be = -1/2, or the neg. recip. of 2 ( which is the slope of the given line - which is already of the form y=mx+b, where m is the slope and b is the y intercept). since the desired line will pass through (-9,6), we just substitute these values for x and y in the equation, and solve for the new 'b' and we get:
(6) = -1/2 (-9)+b and b = 3/2
thus, the equation of the perpendicular line through (-9,6) is:
y= -1/2x +3/2
for parallel lines, they have the same slope. again the slope of the given line is 2, and the y intercept is given already (8). hence the parallel line will have the equation y=2x+8.

Answer 4

for the first one you know that the slope of a perpendicular line is a negative reciporical so the slope (m) is -1/2. You know the coordinates so you can sub those in for the x and y values but you don't know the y-intercept so...
y=mx+b you need to solve for b and you know y, x, and m
6=y (it's the y coordinate your line is going through)
-9=x(it's the x coordinate your line is going through)
and you know m=-1/2 (that's the slope of the new perpendicular line.
6=-1/2(-9)+b
6=4.5+b
subtract 4.5 from both sides
b=1.5
so to write an equation you leave the x and y values as variables and put in your m and b values so:
y=-1/2x+1.5

the next one, you know the y intercept (or b) is 8 and because it's a parallel line, the slope (or m) stays the same so you now have:
y=2x+8. All you had to do was put in the new b value

Answer 5

perpendicular is the opposite reciprocal of the slope

so for 1 a) the slope here is 2
so the perpendicular slope would be -1/2
so using the point slope
y=-1/2x + ?
6=(-.5)*(-9) + ?
6=4.5 + ?
?= 1.5
so the equation is y = -1/2x + 1.5

for 1b
the slope stays the same for parallel
so do the above with without the first part of opposite reciprocal
y intercept of 8 means is passes through (0,8)

try doing the rest by yourself

Answer 6

1a)
First find out the slope of the given line.

The eqn of given line is in standard form, y = mx + b

where m = slope and b is y-intercept

so in the given line, y = 2x - 5

slope, m = 2

The product of slopes perpendicular lines is - 1

So if the slope of required line is m1

m1* 2 = -1

m1 = -1/2

The equation of line with slope m1 and passing through x1, y1 is

y - y1 = m1(x - x1)

here m1 = -1/2, x1 = -9 and y1 = 6

so the equation of required line is

y - 6 = -1/2(x + 9)

2y - 12 = -x - 9

2y = - x + 3

1b)

the slope of given line = 2

since parallel lines will have same slope, the equation of required line has also a slope of 2

y = mx + b

where m is slope and b = y-intercept

here m = 2 and b = 8

the equation of required line is

y = 2x + 8

Answer 7

1a) the slopes will be opposite recipicles (x/y >>> -y/x)

1b) the slopes will be the same since it is parallel. so the equation would be y=2x+8

Answer 8

1a. (y-6)/(x+9) = -1/2
2y-12 = -x - 9
2y + x = 3

1b. y = 2x + 8