Question

How do you graph `y=1/4x-3` by plotting points?

Answer 1

See below.

Explanation:

`y = 1/4x-3`

We know that the equation of a straight line with slope `(m)` and `y-`intercept `(c)` is: `y=mx+c`

Hence, in this example we have a linear function `(y)` with slope `1/4` and `y-` intercept `-3`

To graph a straight line by plotting points only requires two distinct points.

Since the `y-`intercept is `-3` we already know that the point `(0, -3)` is on the line.

Now let's find the `x-`intercept, where `y=0`

`0=1/4x-3`

`1/4x = 3`

`x=12 -> (12,0)` is on the line.

Now we can plot the two points: `(0,-3) and (12,0)` and draw a straight line between them and extending indefinitely in both directions, as shown below.

graph{(y-(x/4-3))(x^2+(y+3)^2-0.1)((x-12)^2+y^2-0.1)=0 [-11.35, 20.67, -7.3, 8.72]}