5.7.1 Ax + By = C Form (standard form)

Remember slope intercept form? y = mx + b This equation gives a lot of information about slope and intercept Good for some real life applications Integers  { . . . -3, -2, -1, 0, 1, 2, 3 . . .}

Standard Form Ax + By = C where A, B, and C are integers Where (0, )  y-intercept And Where ( , 0)  x-intercept y-intercept X-intercept

Similarities Both are great for graphing equations of a line. Graph y=mx +b using slope and y-intercept Graph Ax + By = C using two intercept method.

Differences y=mx +b gives slope information which is nice for many applications we have seen, usually when time is a variable Ax + By = C gives two intercepts which is useful for other types of applications, usually when time is not a variable (maximization problems)

Finding the slope For Ax + By = C The slope is:

Graphing (problems 1-11, 15-22) Ex) x + y = 2 A = 1 B = 1 C = 2 x intercept  ( , 0)  (2, 0) y intercept  ( 0, )  (0, 2)

Point Slope form (problems 24 – 31) Given a point and the slope: m = 6; (3, 4) Use the point slope form of the equation: y – 4 = 6(x – 3) y – 4 = 6x – 18 y – 6x = -14

Homework p. 248 1-3, 5 – 13 odd, 21 – 27 odd, 33, 35