We can analyze demand and supply and market equilibrium with linear equations. These are equations of the form y = a + bx where a is the y-intercept, i. e. , the value of y when x is zero, and b is the slope (rise/run = d y/d x) of the function. We know that the function is linear, i. e. , a line, because the slope is constant. The slope is negative the y falls with an increase in x and is positive if y increases with an increase in x. Example: suppose that the following equations describe the market demand for and supply of a. Supply: ps = 30 + 0. 1qs (p is in and q is in units) We don"t need to label these equations demand and supply since the negative slope of the first one and the positive slope of the second one tell us that they are demand and supply respectively.