Question

Write the equation of the line that passes through (1, 5) and (−2, 14) in slope-intercept form.

Answer 1

@jim_thompson5910

Answer 2

A. y = 3x + 2
B. y = 3x + 8
C. y = −3x − 2
D. y = −3x + 8

Answer 3

what is the change in y when we go from y = 5 to y = 14 ?

Answer 4

I have no idea.

Answer 5

subtract the values to find out

Answer 6

9?

Answer 7

yes, now what is the change in x when we go from x = 1 to x = -2 ?

Answer 8

-3?

Answer 9

yes -2-1 = -3

Answer 10

change in y = 9
change in x = -3

divide the two values: 9 divided by -3 = -3

so the slope here is -3

Answer 11

So, it's either C or D?

Answer 12

yes

Answer 13

the slope is m = -3

we replace m with -3 in y = mx+b

so y = mx+b turns into y = -3x+b

Answer 14

now pick one of the two points, say (1,5)

the first coordinate is x, which means x = 1
the second coordinate is y, so y = 5

you plug x = 1 and y = 5 into y = -3x+b to get


y = -3x+b
5 = -3*1+b

now isolate b

Answer 15

So, you just have, 5=-3*1?

Answer 16

5 = -3*1+b turns into 5 = -3+b

which is the same as 5 = b-3

Answer 17

you have to solve for b now

Answer 18

How do you do that?

Answer 19

how would you undo that -3 ?

Answer 20

Dividing?

Answer 21

addition is the opposite of subtraction

Answer 22

So we add?

Answer 23

So, would it be, D. y = −3x + 8?

Answer 24

yes add 3 to both sides and you end up with b = 8

so the final answer is y = -3x+8

Answer 25

Thank you!!

Answer 26

no problem