Question

Find the equation of a line that passes through the points (-3,6) and (1,2) then sketch the line.

Answer 1

@Easyaspi314

Answer 2

To write the equation of a line, we need slope.

The slope between two points is the difference between the y-values divided by the difference between the x-values.

So the slope between (-3,6) and (1,2) is
(2-6)/(1- -3) = -4/4 = -1

So we know that the line we want has a slope of -1.

Answer 3

Now, to write the equation of the line, we know that a line has the form y = mx + b, where m = slope and b = y-intercept.

So we need m and b.

We know that the slope, m, is -1.

All what we need is to find b, and we are done.

Answer 4

To find b, take ANY of the two points, say

Answer 5

y=-1x+b

Answer 6

(1,2) and plug it into the equation to find b.

y = 1x + b
Substitute y = 2 and x = 1

so, 2 = 1(1) + b
2 = 1 + b
b = 1

Therefore, the equation of the line is y = x + 1.

Done.

Answer 7

Makes sense?

Answer 8

yes

Answer 9

can you sketch?

Answer 10

My error...slope was -1, not 1.

Answer 11

So it's y=-x+b?

Answer 12

I mean y=-x+1?

Answer 13

So the equation is y = -1x + b

Substitute x = 1 and y = 2, we get

2 = -1(1) + b
2 = -1 + b
b = 3

So the equation of the line is y = -x + 3.

Done!

Answer 14

Makes sense?

Answer 15

Yes, can you sketch it plz?

Answer 16

Yes. just plot the two points (1,2) and (-3,6) and connect the line. So straightforward. I know you can do that.

Answer 17

Yes that's easy, thanks for the help!

Answer 18

See the line?

Answer 19

By the way, to better your understanding.....notice from left to right, the line is "falling"...and that is what negative slope looks like. If the slope would be positive, then from left to right, the line would be inreasing, not decreasing like our line.

Answer 20

I understand, thank you (:

Answer 21

You're welcome.