In this problem you are looking at a linear equation in two variables (x and y). This is an equation which can be written in the form Ax + By = C. You can see this by writing it as 1x + (-2)y = 8, so that A = 1, B = -2, and C = 8. It is called a linear equation because the graph of this kind of equation is a straight line, if it exists.
To write this equation in slope-intercept form, just manipulate it so that y is isolated on one side of the equation (this is the same as solving for y), like this:
This is called the slope-intercept form because it displays the slope of the straight line determined by this equation (the coefficient of x, which is 1/2 in this case), and the y-intercept (the y-value where the graph intercepts the y-axis, which is -4 in this case). Consult your textbook or speak with your teacher or fellow students for more information about this type of equation.
To graph a linear equation in two variables, you really only need two points. One point, the y-intercept, is given by setting x to 0 and solving for y:
The y-intercept is therefore (0,-4) since, when x=0, y=-4.
A second point is given by setting y to 0 and then solving for x:
The x-intercept is therefore (8,0) since, when y=0, x=8.
Now that you have two points, you can just plot them on a pair of coordinate axes and draw the straight line that goes through both of them (there can only be one).
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