5x + 2y = 10 represents a line on the x-y coordinate system. I find it useful when I have a linear equation to put it in y = mx + b form, because in that form we know that m is the slope of the line (rise/run) and b is where the line crosses the y -axis. With this information, it's much easier to graph the line. We start with your equation, and try to get y on a side by itself:5x + 2y = 10 (subtract 5x from both sides)2y = -5x + 10 (divide both sides by 2)y = (-5/2)*x + 5 So now we know that the line crosses the y axis at 5, and slopes downward with a slope of -5/2. You can just put your pencil at the 5 on the y-axis, and then count down 5 and to the right two, and draw a dot there. Then draw a line with your ruler that passes through the 5 on the y-axis and also through the dot you just drew. y = -6 is just a horizontal line through the -6 on the y-axis. If you think about this as being in the y = mx + b form, b = -6, so that's the y - intercept, and m is 0. No slope!
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