Question

Write a equation that relates y to x, in point-slope form.
Here's the table
X| 2 |4| 6 | 9 |11
Y|-3|5|13|25|33
(is there anyway to post a picture of the graph? Hatching here! First post/question)

Answer 1

Never mind about the picture! I figured out I can add a picture in a reply. Here's the graph!

Answer 2

The equation we'll be using here is:
\[y-y_1=m(x-x_1)\]Where m is the slope of the line, and x_1,y_1 are the coordinates of any point on the line.

You'll want to start out by finding the slope between any two points on that graph. Can you figure out the slope using the table?

Answer 3

How do you solve slope?

Answer 4

is it Y=mb?

Answer 5

sorry Y=mx+b

Answer 6

To find the slope between two points, divide the difference in their y values by the difference in their x values:
\[m=\frac{ \Delta y }{ \Delta x }=\frac{ y_2 - y_1 }{ x_2 - x_1 }\]

Answer 7

ok thanks...I don't remeber what y2/y1 and x2/x1 corespond to. I should be able to figue it out with those though

Answer 8

Pick any two points from the table. Call one of them point 1, and one of them point 2.

Then x_1 is the x coordinate of point 1, y_1 is the y coordinate of point 1, and so on for point 2.

Answer 9

ok so It can be any two points? so it can be 9-4/25-5

Answer 10

Right, but you have the fraction upside down. It should be 25-5 / 9-4

Answer 11

thanks
That leaves me with 20/5 which = 4

Answer 12

So my slope would equal 4

Answer 13

Exactly. So lets go back to our equation for the line:
\[y-y_1=m(x-x_1)\]Now, since m is the slope, plug in m=4. Now, you can pick any one point, and plug in its x and y coordinate as x_1 and y_1 and you're done

Answer 14

so that means I'm left with 25-5=4(9-4)

Answer 15

so I have 20=20

Answer 16

Which leaves me with 0?!

Answer 17

In this equation, you only plug in one point. So use the point (9,25). Now plug in x_1=9 and y_1=25. The x and y without the subscript stay x and y.
\[y-y_1=4(x-x_1)\]

Answer 18

ok So that leaves me with y=25=4(x-9)

Answer 19

So that would be my equation in point-slope intercept form? My answer?

Answer 20

y-25=4(x-9) is the equation of our line. You can leave it in this form, or you can put it in y= form by adding 25 to both sides.

Answer 21

OK thank you!

Answer 22

No problem, glad I could help

Answer 23

OK Just to be sure my equation in Y=mx+b would equal y=4x-11

Answer 24

Yep, exactly

Answer 25

Thanks :) Sorry it took so long! I think I get the concept now

Answer 26

No problem, and great, thats what we're here for