Question

Which equation represents the values in the table? x–1012y–13711A.y = 4x + 3B.y = −x − 1C.y = 3x − 1D.y = 1/4x − 3/4

Answer 1

We know it's a linear function, which is like

`f(x)=mx+b`

We can find the slope "m" of the linear function doing

`m=(y_2-y_1)/(x_2-x_1)`

There the points x₂, x₁, y₂ and y₁ we can take what's more convenient for us, just be careful, if you do x₁ = 0, you must take the correspondent y₁, the value of y on the same column, therefore y₁ = 3, for example.

I'll do x₁ = 0 which implies y₁ = 3 and x₂ = 1 which implies y₂ = 7. Therefore

`\begin{gathered} m=\frac{7_{}-3}{1_{}-0_{}} \\ \\ m=\frac{7_{}-3}{1_{}}=4 \end{gathered}`

Therefore the slope is m = 4, then

`y=4x+b`

To find out the "b" value we can use the fact that when x = 0 we have y = 3, therefore

`\begin{gathered} y=4x+b \\ \\ 3=4\cdot0+b \\ \\ 3=b \\ \end{gathered}`

Then b = 3, our equation is

`y=4x+3`

The correct equation is the letter A.