Question

Write an equation in slope-intercept form for the line that is perpendicular to the given line and that passes through the given point.

1) 2x+3y=7; (4,5)
2) -2x - 8y= 16; (4,5)
3) y = x -5; (0,5)

Answer 1

perpendicular line will have a slope that is the negative reciprical of the given line

Answer 2

for example #3

y = x - 5
Slope = 1

Perpendicular slope -1

Answer 3

Use point-slope formula to make a line equation from a point (x1,y1) and a slope (m)

y - y1 = m*(x-x1)

Answer 4

To begin #1, write 2x + 3y = 7 in y = m*x + b form

Answer 5

So what does the b stand for? and how do we know what to put there?

Answer 6

Slope-Intercept form of a line
y = m*x + b

m = slope
b = y-intercept

Answer 7

Okay that makes sense..

Answer 8

1) 2x + 3y = 7

Rearrange to the form , y = m*x+b

3y = -2x + 7

y = (-2/3)*x + (7/3)

Slope m = -2/3
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A line perpendicular to that line will have a slope that is the negative reciprical of -2/3

Slope of perpendicular line = +3/2

Answer 9

The equation for the perpendicular line will be:
slope m = 3/2
point (x1,y1) = (4,5)

y - y1 = m*(x-x1)
Plug in the values

y - 5 = (3/2)*(x - 4)

Answer 10

You can clean that up a little if you want, distribute the 3/2 into the x-4 and add 5 to both sides...

y - 5 = (3/2)x - 4*(3/2)

y = (3/2)x - 6 + 5

y = (3/2)*x - 1

Answer 11

same process for the next 2 probs.

Answer 12

Okay, thank you so much for your help! Your a life saver!

Answer 13

You're welcome. Does it make sense now?

Answer 14

Yes, you make way more sense then my math teacher does!

Answer 15

haha, if you want to try and work through #2, i can check if it is right, for practice if you want

Answer 16

Okay, would #2 be y= 2/8*x-1?

Answer 17

2) -2x - 8y= 16; (4,5)

rearranging: y = (-1/4)x - 2
Slope = -1/4
------------------------------

Perpendicular Line:
slope m = 4
point (x1,y1) = (4,5)

y - y1= m(x - x1)
y - 5 = 4*(x - 4)
y - 5 = 4x - 16
y = 4x - 11
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The Line; y = 4x - 11, is perpendicular to the line -2x-8y=16, and goes through the point (x,y) = (4,5)

Answer 18

Graph