Reference no: EM132012440

• Because the variable m does not appear in Ax + By = C, equations in this form make it impossible to determine the line's slope m.  If the statement does not make sense, then how can you find m and what would it be? 
• If I drive m miles in a year, the formula C = 0.25x + 3,500 models the annual cost, C, in dollars, of operating my car, so the equation shows that (a) with no driving at all, the cost is $3,500, and (b) the rate of increase in the cost is $0.25 for each mile I drive.  

Equation of a line may be represented in the form Ax+Bx=C, y=mx+b, and many other forms. For example, 5x+3y=15 and y=(-5/3)x+5 represent the exact same line.  Every line has a unique and y-intercept (except for the vertical lines that do not intercept the y axis).  The main idea behind this assignment is to realize that regardless of which form of the equation is used, you should be able to solve the equation for y (except for vertical lines) and find the slope and the y-intercept.  When the equation is put in the form y=mx+b, then the numerical coefficient of x is the slope and the number b is the y-intercept. In this case, we have:

Ax+By = C

By = -Ax + C

y = (-A/B) + (C/B)

so: slope = (-A/B) and y-intercept = (C/B)