How do i graph 4x - 8y = -16 ?

Question

I am given an equation of 4x - 8y = -16, and all I know is that I need to find the x and y coordinates to be able to graph it, but im not sure how. This is 8th grade pre-algebra. 

Answer 1

4x - 8y = -16

 

Since this represents a straight line, you need 2 points to graph it.  Just draw a straight line passing through the 2 points.  The easiest points to find are the x and y intercepts.

 

x intercept:

 

y = 0

4x - 8(0) = -16

4x = -16

x = -4

The x intercept is (-4,0)

 

y intercept:

 

x = 0

4(0) - 8y = -16

-8y = -16

y = 2

The y intercept is (0,2)

 

Draw your x-y axes, label the points (-4,0) and (0,2), draw a straight line through these 2 points, and you have your graph.

 

Answer 2

My favorite way is to solve for y and put it into y = mx+b form

 

Subtract 4x from both sides

-8y = -16 - 4x

 

Divide by -8

y = 2 + x/2

 

Now I have a line with a Y intercept of 2 and a slope of 1/2

 

HOWEVER since this is 8th grade pre algebra, they're forcing you to learn "annoyingly difficult" form:

 

4x - 8y = -16

 

Plug in x=0

4*0 - 8y = -16

-8y = -16

y = 2

So when x is 0, y is 2

 

Plug in y=0

4x - 8*0 = -16

4x = -16

x = -4

when Y is 0, x is -4

 

Plot the points (0,2) and (-4,0)

 

For the slope, you do -1 * coefficient of X / coefficient of Y

x's coeff is 4, y's coeff is -8

so -1 * 4 / -8 = 4/8 = 1/2