Question

which of the lines graphed in the diagram represents the equation 6x + 4y = 8

Answer 1

In order to easily discern which graph is a proper representation of 6x + 4y = 8, you first need to convert the equation to y = mx+ b, also known as slope-intercept form. Here's how you can do this:
6x + 4y = 8
4y = -6x + 8
y = -1.5x + 2
The +2 tells you that your line will intercept the vertical y-axis at (0, 2). This narrows it down to graphs a and d. Then, because you have a NEGATIVE number in front of your x (it's -1.5), you can tell that your graph will be going down as it moves from left to right. This leaves you with graph d as your answer!

Answer 2

To find which line is which, let's turn that equation into slope intercept form:

6x + 4y = 8

Subtract 6x from each side:

4y= -6x + 8

Then divide both sides by 4:

y= -6/4x + 2

With slope intercept form, y=mx+b, we know that b is the y-intercept. 

If 2 is our y-int, the we know the it is not the vertical line because it doesn't touch (0,2)

Now, we also now that our line is negative because our x is negative, so that means the line goes from to down and to the right.

So that means it's the line (-3,5)

Hope this helps!