Parallel and Perpendicular lines?

Question

Find the equation of the line that is parallel to y -2x = 3 and passes through the point (2, 5).

Find the equation of the line perpendicular to y -2x = 3 and passing through the point (2, 5).

Answer 1

First, change the equation to slope-intercept form.

y - 2x = 3
y = 2x + 3

Now, we can see that the slope is 2.

A line parallel to that line will have the same slope (2). A line perpendicular to that line will have a slope of (-1/2) - the opposite reciprocal.

So, use point-slope form to find the equations you're looking for.

y - y1 = m (x - x1)

where m is the slope and (x1, y1) is the given point.

Parallel thru (2, 5):
y - 5 = 2(x - 2)
y - 5 = 2x - 4
y = 2x + 1 (in slope intercept form)
-2x + y = 1
2x - y = - 1 (in standard form)

Perpendicular thru (2, 5)
y - 5 = (-1/2)(x - 2)
y - 5 = (-1/2)x + 1
y = (-1/2)x + 6 (in slope intercept form)
2y = -x + 12
x + 2y = 12 (in standard form)

Answer 2

okay for the first question we need to find an equation that is parallel and passes through that pt. Now the eq. of a line is y=mx+b. Since they are parallel they share the same slope or m.
To solve this we replace y with 5 and x with 2 in the equation and m is 2
5=2(2)+b so b is 5-4 or 1 so your equation becomes y=2x+1

2nd one take similar approach except perpendicular lines have negative reciprical. so in this case m = -1/2
5=-1/2(2)+b solve for b you get 6 so the equation is y=-1/2+6

Answer 3

Find the equation of the line that is parallel to y -2x = 3 and passes through the point (2, 5).

y-5=2(x-2).
Parallel and Perpendicular lines?
Find the equation of the line that is parallel to y -2x = 3 and passes through the point (2, 5).

Find the equation of the line perpendicular to y -2x = 3 and passing through the point (2, 5).
slope of perpendicular line=-1/2
the equation of the perpendicular line:
y-5=-1/2(x-2). answer

Answer 4

You should know this stuff.
In both cases, rewrite the equation given to
.....y= 2x+3. Then it''s slope is 2.

In the first case, the line you want will have a slope of 2. To find the y-intercept (the +3 above), you substitute. Write 5 = 2*2 + b and b= 1. So y= 2x+1

In the second case, the line you want will have a slope of MINUS THE RECIPROCAL of 2 or -1/2. You find the y intercept the same way, substitute.

Answer 5

y=2x+b
you are trying to find b, so you plug in the given points. y=5 and x=2

5=2(2)+b
5-4=b
1=b
so the parallel line would be y=2x+1

To find the perpendicular line, you do the same as above. The only difference is that you must change the slope of the line to -1/2x

y=-1/2x + b
5=-1/2(2) +b
5= -1 +b
5+1 = b
6= b
y= -1/2x + 6

Answer 6

Line with the same gradient is y - 2x = c

Passes through x = 2, y = 5 so 5 - 4 = c

c = 1

Line is y - 2x = 1

Perpendicular line is y + ½x = c

5 + 1 = c = 6

Line is y + ½x = 6

Answer 7

Question 1
y = 2x + 3
m = 2
Equation of parallel line is:-
y - 5 = 2.(x - 2)
y = 2x + 1
Question 2
y = 2x + 3
Perpendicular line has m = - 1/2
y - 5 = (- 1/2).(x - 2)
y - 5 = (- 1/2).x + 1
y = (- 1/2).x + 6

Answer 8

12x + 4y = sixteen 4y = sixteen - 12x y = -3x + 4 slope m1 = -3 (y = mx + c) 5y - 22 = -15x y = -3x + 22/5 slope m2 = -3 to that end, the two lines are parallel to a minimum of one yet another considering they have comparable slope

Answer 9

i dont want to but i think its 2