In a linear equation that shows a direct relationship, as the x-values go up, so do the y-values. The equations y = x, y = 3x + 6, and y = 8x - 10 all feature direct relationships. If you plug in rising x-values, you'll notice that the corresponding y-values also increase.
Linear equations expressing inverse relationships slope in the opposite direction from direct relationship equations. As x-values increase, y-values decrease. The equations y = -x, y = -3x + 4, and y = -1/2x - 1 all feature inverse relationships. Rising x-values will result in decreasing y-values.
Linear equations with direct relationships all have positive slope -- a term referring to a line's tendency to rise or fall over time. The standard equation for a line is y = mx + b, where m tells you the slope of the line.
For the equation y = x, m = 1. Therefore, for every one-unit increase in x, y will also increase by one unit. For the equation y = -2x + 1, for every one-unit increase in x, y will decrease by two units.
In the standard equation for a line (y = mx + b), the "b" refers to the y-intercept -- the point where the line crosses the y-axis. In the equation y = x, the line crosses the y-axis at y=0 (and also at x=0, since y = x). In the equation y = -1/2x - 6, the line crosses the y-axis at y=-6. The y-intercept means the same thing whether you're working with a direct-relationship or inverse-relationship linear equation.