# How do you graph y=x+12 and y=1/4x-3?

See below:

#### Explanation:

Each of these equations is a line. Let's do them one at a time, then combine them.

$y = x + 12$

For this, we can draw a line with the $y$-intercept at 12 $\left(0 , 12\right)$ and then with the slope being 1, we can also draw in a point at $\left(0 + 1 , 12 + 1\right) \implies \left(1 , 13\right)$, connect the dots and draw the line.

graph{x+12 [-20.58, 7.9, -0.82, 13.42]}

$y = \frac{1}{4} x - 3$

We can graph the $y$-intercept point $\left(0 , - 3\right)$ and with slope $\frac{1}{4}$ we can also graph $\left(0 + 4 , - 3 + 1\right) \implies \left(4 , - 2\right)$, connect them up and draw the line.

graph{1/4x-3 [-7.77, 24.27, -7.41, 8.61]}

Put them together and we have:

graph{(y-(x+12))(y-(1/4x-3))=0 [-24.43, 4.04, -12.2, 2.04]}