Question

How do you graph `f(x)= 1/4x + 8` by plotting points?

Answer 1

See explanation.

Explanation:

To pliot a linear function you only need 2 points. So the easiest way to plot a function is to substitute 2 integers to calculate the points.

`f(0)=1/4*0+8=8`

Since there is a denominator `4` it will be easier to substitute `4`

`f(4)=1/4*4+8=1+8=9`

Now we can draw the function.

graph{(y-1/4x-8)(x^2+(y-8)^2-0.5)((x-4)^2+(y-9)^2-0.5)=0 [-32.47, 32.46, -16.23, 16.25]}

Answer 2

A quick and easy way to graph a line is to plot the `x` and the `y` intercepts.

Explanation:

The intercepts lie on the line where one of the values is `0`.
That makes it easy to solve for the other value just by looking -- no math necessary.
.......................

The `y` intercept must be the place where `x` equals `0`, which is the ordered pair `(0,y)`

To let `x` equal `0`, just put your fingertip over the `mx` term and hide it.
It would have dropped out to zero anyway.
Then solve the equation in your head.
`f(x)=(1)/(4)x+8`

Cover the `mx` term (which is zero) with your fingertip and solve for `y`
`f(x)=` ░░ `+8`

This gives you the ordered pair `(0,8)`, which is tthe `y` intercept.
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The `x` intercept must be the place where `y` equals `0`, which is the ordered pair `(x,0)`.

To find this point rapidly, cover the `y` term with your fingertip.
It would have ended up as zero anyway.
Then solve for `x` in your head.

░░ `=(1)/(4)x+8`
`- 32 = x`

This gives you the ordered pair `(-32,0)`, which is the `x` intercept.
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Now you have two useful ordered pairs that you can find without doing any math.

`(0,8)` `larr` the `y` intercept
`(-32,0)` `larr` the `x` intercept