To graph a function in the x-y plane, we need to isolate y on one side of the equation, then we have to replace some values of x and calculate the values of y, once we have two points, we can plot them and join them, in this case, we can do it like this:
y - 2 = 1/5 (x-4), by distributing the product on the right side, we get:
[tex]\begin{gathered} y-2=\frac{1}{5}\times x-\frac{1}{5}\times4 \\ y-2=\frac{x}{5}-\frac{4}{5} \end{gathered}[/tex]By adding 2 on both sides of the equation:
[tex]\begin{gathered} y-2=\frac{x}{5}-\frac{4}{5} \\ y-2+2=\frac{x}{5}-\frac{4}{5}+2 \\ y=\frac{x}{5}-\frac{4}{5}+2 \\ y=\frac{x}{5}-\frac{4}{5}+2\times\frac{5}{5} \\ y=\frac{x}{5}-\frac{4}{5}+\frac{2\times5}{5} \\ y=\frac{x}{5}-\frac{4}{5}+\frac{10}{5} \\ y=\frac{x}{5}+\frac{10-4}{5} \\ y=\frac{x}{5}+\frac{6}{5} \end{gathered}[/tex]Now that we know the equation of y as a function of x, we can see that we have a linear function, when we have a line we only need to find two points of the line and then join them with the line.
Let's take for example x equals 4, then:
y(4) = 4/5+6/5 = 4/5+6/5 = 10/5 = 2 , then we have the point (4,2)
and with x equals -1:
y(-1) = -1/5 + 6/5 = 5/5 = 1, then the line has the point (-1,1)
Now, let's locate these points in a graph and then join them with the line:
