Question

Graph each lineY + 3 = 1/4(x - 4)X = 3

Answer 1

We have two expressions to graph, we'll start with the easiest one this is x = 3

x = 3 represents a continuous line that passes through all points when x has a value of 3, i.e. a vertical line through the point when x is 3

For the other equation to be graphed, let's first solve this one by simplifying it

`\begin{gathered} y+3=(1)/(4)(x-4) \\ y+3=(1)/(4)x-(4)/(4) \\ y=(1)/(4)x-1-3 \\ y=(1)/(4)x-4 \end{gathered}`

In conclusion, the equation of the simplified line is:

`y=(1)/(4)x-4`

To determine the values and graph this equation we must take values of "x" and replace them, the result when replacing these values will form the coordinates that we must locate in the Cartesian plane

Next, we will make a few points

`\begin{gathered} x=8 \\ y=(1)/(4)\cdot(8)-4 \\ y=2-4 \\ y=-2 \end{gathered}`

`\begin{gathered} x=-8 \\ y=(1)/(4)\cdot(-8)-4 \\ y=-2-4 \\ y=-6 \end{gathered}`

Therefore, the line passed for (-8,-6) and (8,-2)

Below is a graph that shows how both equations are plotted and that the equation of the line passes through these two points