Question

How do I find the equation of a line from the table
X= 2,4,6,8,10,12,14
Y= 1,6,11,16,21,26,31 ?

Answer 1

Well, you can start off by finding the slope. This can be done by just pickign two points and plugging them into the slope formula. So one point is (2,1) and the next point is (4,6). So I can plug those in and get:

\[\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }=\frac{ 6-1 }{ 4-2 }=\frac{ 5 }{ 2 } \]So this means our slope is (5/2) So we have a slope and we have a point. This allows us to use point-slope form to calculate the equation. Now, the equation requires that I use x1 and y1, meaning I can't just pick any point, I MUST pick the (x1,y1) point. In this case, that point was (2,1), so this is the point Ill plug into the formula. The point-slope formula is this:

\[y-y _{1}=m(x-x _{1})\]where y1 is the y-coordinate, x1 is the x-coordinate and m is the slope. So plugging these values into the formula I have:

\[y-1 = \frac{ 5 }{ 2 }(x-2)\]
\[y-1 = \frac{ 5x }{ 2 }-5\]
\[y=\frac{ 5x }{ 2 }-4 \]

And that would be your answer.

Answer 2

thank you so much for explaining it!! :)

Answer 3

Yeah, np :3

Answer 4

@Psymon now that i have the slope, how would i write the equation of the linear function represented by the table in point-slope form? :o

Answer 5

It was a part of my steps actually xD I used point-slope form to get the equation in the first place.

Answer 6

\[y-y _{1}=m(x-x _{1})\]Plugging in the numbers I got:
\[y-1 = \frac{ 5 }{ 2 }(x-2)\]

Answer 7

so would y−1=5/2(x−2) be the answer for that last question or would it just be y=5/2x-4? :p

Answer 8

Sorry, I wasnt able to be here, Im at school and couldnt respond. But yopu would keep it the first one, if you multiply it out its slope intercept

Answer 9

its okay! i completely understand, just this year i started an online home school thing because of a few medical conditions :p but i found the answer after i reread what you put earlier! thanks :)