Question

What is an equation for the linear function whose graph contains the points  ( −1, −2

)  and  ( 3, 10 )  ?

Enter your answers in the boxes.

Answer 1

There are two ways to equate a straight line. We first have y=mx+b. Then, we have (y-y₁)=m(x-x₁). Both work fine and have similar variables, but the numbers are mixed around a bit. Your equation clearly shows the second form of equation. As our equation has x-x₁ on the right, we can notice that x+1 must mimic that, so x+1=(x-x₁). As x-(-1)=x+1, we can only assume that x is -1. Looking at the points given to us, y must be -2, so we have y-(-2)=y+2, so 2 fills in the leftmost open box. To find the slope, or m, we must take

`((y_(1) -y_(2)))/((x_(1) -x_(2)))` from points (x₁, y₁) and (x₂, y₂). It doesn't matter which point is (x₁, y₁) , but it matters that the y₁ corresponds to the x₁. Thus, we have our slope as
`(-2-10)/(-1-3) =(-12)/(-4) =3`

Feel free to ask further questions, and Happy Halloween!

Answer 2

Answer: y+2=3(x+1)

so the first box you would put 2 and then the second box you would put 3!