How do you graph f(x)= 1/4x + 8 f(x)=14x+8 by plotting points?

2 Answers
Nov 25, 2017

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=8f(0)=140+8=8

Since there is a denominator 44 it will be easier to substitute 44

f(4)=1/4*4+8=1+8=9f(4)=144+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]}

Nov 25, 2017

A quick and easy way to graph a line is to plot the xx and the yy intercepts.

Explanation:

The intercepts lie on the line where one of the values is 00.
That makes it easy to solve for the other value just by looking -- no math necessary.
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The yy intercept must be the place where xx equals 00, which is the ordered pair (0,y)(0,y)

To let xx equal 00, just put your fingertip over the mxmx term and hide it.
It would have dropped out to zero anyway.
Then solve the equation in your head.
f(x)=(1)/(4)x+8f(x)=14x+8

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

This gives you the ordered pair (0,8)(0,8), which is tthe yy intercept.
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The xx intercept must be the place where yy equals 00, which is the ordered pair (x,0)(x,0).

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

░░ =(1)/(4)x+8=14x+8
- 32 = x32=x

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

(0,8)(0,8) larr the yy intercept
(-32,0)(32,0) larr the xx intercept