Finding Slope and Y-Intercept for Points on a Line: A Simple Explanation

[Doomkiin]

Hey so I have a math test tomorrow and I'm really good in math, I just need some small clarification, so here's my problem.

V(-2,k) P(4,9) slope of 2/3

so I decided to find y=mx+b with P(4,9) because after I find B I could do the same with V(-2,k)

so I did the equation and B came up 7, so next I decided to do.


y=2/3(-2)+7

but I got, y=17/3

However in the optional choice there's only -5, 3, 5 and 7 I asked my friend and he said it was 5 but I didn't really understand his explanation so I would really appreciate some deeper or simple explanation please, my friend also told me that the way I was doing it wouldn't work and I was just wondering as to why not ?

thank you for your time.

ps: It may not be called a slope but I come from a french school and that was the translation I came up with.

 

[Einj]

You got the wrong value for b. As you said $y=\frac{2}{3}x+b$. If you use the first point you have:
$$
9=\frac{2}{3}\cdot 4+b\implies b=9-\frac{8}{3}=\frac{19}{3}.
$$
So $y=\frac{2}{3}x+\frac{19}{3}$. Lastly, plugging x=-2:
$$
y=\frac{2}{3}\cdot(-2)+\frac{19}{3}=\frac{-4+19}{3}=\frac{15}{3}=5.
$$
I hope this is clear.

 

[verty]

Or you could do it in one step using the point-slope formula and entering both points.