Question

Which is the graph of the equation y-1= 1= (x-3)? у 8 4 . -10-3 A-22 3 6

Answer 1

First of all, we need to write the equation given:

$y-1=\frac{2}{3}(x-3)$

We solve that equation to y like this:

$\begin{gathered} y-1=\frac{2}{3}(x-3) \\ y=\frac{2}{3}x-3\cdot\frac{2}{3}+1 \\ y=\text{ }\frac{2}{3}x-2+1 \\ y=\text{ }\frac{2}{3}x-1 \end{gathered}$

To draw that we need to find two points and make a line join together those poins.

We start to x=0, like this:

$\begin{gathered} y=\text{ }\frac{2}{3}x-1;\text{ x=0} \\ y=\frac{2}{3}(0)-1 \\ y=-1 \end{gathered}$

Then the first point is (0,-1)

For the second point we make y = 0, then:

$\begin{gathered} y=\frac{2}{3}x-1;\text{ y=0} \\ 0=\frac{2}{3}x-1 \\ 1=\frac{2}{3}x \\ \frac{3}{2}=x=1.5 \end{gathered}$

Now, the second point will be (3/2,0)

Finally, we put that on a graph and compare with your options...

That will be the draw.. and from your options...