Question

Write an equation of the line through the
point (a) parallel to the given line and (b) perpendicular to the given line. point: (-3, 2) line: x+y=7

Answer 1

@Easyaspi314

Answer 2

For part (a), we want to write the equation of the line through the point (-3,2) and parallel to the line x + y = 7.

Answer 3

Note, that our line will be parallel to the line x + y = 7, so the slopes MUST be equal.

Answer 4

Okay

Answer 5

Let's figure out what the slope of the line x+ y = 7 is.

Answer 6

-x?

Answer 7

write x + y = 7 in the form y = mx+b

so we want to solve for y.

x + y = 7

subtract x from both sides, we get

y = 7 - x

So whats the slope of the line? The slope is m, the coefficient of x. So the slope is -1. Agree??????

Answer 8

Yes

Answer 9

So our line will have a slope of -1.

Answer 10

So the other line must too to be parallel

Answer 11

@Easyaspi314 2=-1(-3)+b?

Answer 12

So we want to write the equation of the line whose slope is -1 and passing through the point (-3,2).

We did write such a line in our last problem, but I will do this one to reinforce the concept.

Since our line has slope -1, the equation is

y = -1x + b

Substitute (-3,2)...that is x = -3 and y = 2 into the equation and solve for b.

Answer 13

b=0?

Answer 14

So y = -1x + b

x = -3, y = 2

so we have 2 = -1(-3) + b
2 = 3 + b

b = -1

So the equation of the line will be y = -x - 1.

Answer 15

oh

Answer 16

To be evry clear, this line y = -x - 1, will pass through (-3,2) and be parallel to the line x+y = 7.

Answer 17

very*

Answer 18

Does part (a) make perfect sense???

Answer 19

Yes

Answer 20

OK..for part (b)...we want to write the equation of the line passing through (-3,2) but perpendicular to the line x + y = 7.

Very similar to part(a).

You must know that any line perpendicular to the line x+y = 7 will have the negative reciprocal slope.

So the negative reciprocal of -2/3 will be +3/2.

The line x+y=7 has a slope of -1, as we did before.

So the line perpendicular to x+y = 7 will have a slope that is the negative reciprocal of -1.

What is the negative reciprocal of -1? It is +1.

So our line will have a slope of 1.

Now, you can write the equation of the line that has a slope of 1 and passing through

Answer 21

the point (-3,2).

Answer 22

You write the equation of the line whose slope is 1 and passing through (-3,2). Then I will see if you are right or wrong.

Answer 23

ok?

Answer 24

?

Answer 25

y=x-1?

Answer 26

Let me see...I didnt do it yet.

Answer 27

ok

Answer 28

I got y = x+5..let me see what you did

Answer 29

ok

Answer 30

slope = 1
passing through (-3,2).

What did you do to write the equation of the line?

Answer 31

I just changed the slope value to positive i didn't know you had to change the y-intercept

Answer 32

watch.......

Answer 33

ok

Answer 34

the general equation of a line is y = mx + b

We have a slope of 1, so m = 1

so we have y = 1x + b

The question is what is b?

so we plug in x = -3 and y = 2 into the above equation...so we get

2 = 1(-3) + b

Now we solve for b...we get

22

Answer 35

froget that 22 at the bottom

Answer 36

we get 2 = -3 + b

b = 5

so the equation of the line will be y = x + 5.

Answer 37

get it? any questions?

Answer 38

I understand thank you!

Answer 39

welcome.