Question

Graph this. y-2= 1/5(x-4)

Answer 1

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:

`\begin{gathered} y-2=(1)/(5)* x-(1)/(5)*4 \\ y-2=(x)/(5)-(4)/(5) \end{gathered}`

By adding 2 on both sides of the equation:

`\begin{gathered} y-2=(x)/(5)-(4)/(5) \\ y-2+2=(x)/(5)-(4)/(5)+2 \\ y=(x)/(5)-(4)/(5)+2 \\ y=(x)/(5)-(4)/(5)+2*(5)/(5) \\ y=(x)/(5)-(4)/(5)+(2*5)/(5) \\ y=(x)/(5)-(4)/(5)+(10)/(5) \\ y=(x)/(5)+(10-4)/(5) \\ y=(x)/(5)+(6)/(5) \end{gathered}`

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: