1. Standard Form Section 6-4

2. Notes Standard Form of a Linear Equation: Ax + By = C where A, B, and C are real numbers.

3. Example We need to graph 2x + 3y = 12 First we need to find the x and y –intercept. Let’s start with the y-intercept:

4. Question In order to find the y-intercept we need to remember what it is. The y-intercept is the location where the line crosses the y-axis and x = 0. So for our equation we need to replace x with 0 and solve for y.

5. Example Now for the x-intercept: So the equation crosses the y-axis at 4 and the x-axis at 6.

6. Graphing

8. Let’s try one from your homework 9.) -8x + 10y = 40 First find the y-intercept when x = 0 Second find the x-intercept when y = 0 Who would like to come up to the board to show us how it’s done?

9. Let’s try one more Write each equation in standard form: Our goal is to get the variables on one side and the constants (numbers) on the other.

10. How about one story problem First thing we need to do is define the variables: r = time running w = time walking Remember D = rt

11. Conclusion We know the distance is 15 miles and if we added up the distances from walking and running we would end up with the total 15 = (walking rate)w + (running rate)r 15 = 3w + 8r