1. Chapter 2 Section 2 Linear Equations Lesson essential question: How can you determine if an equation is linear?

2. Definitions Linear Function: A function whose graph is a straight line. Linear Equation: An equation that represents a linear function There are no exponents on x or y if the equation is linear i.e. y=3x+4. Solution of Linear Equation: Any ordered pair that makes the equation true. i.e. (0,2) is a solution for y=x+2.

3. More Definitions The value of x is whatever we pick, so x is the Independent Variable. The value of y depends on whatever you pick for x. Therefore, we call y the Dependent Variable. Independent Variable. Calls the shots. Dependent Variable. Notorious kiss-up.

4. Intercepts y-intercept: the point at which the line crosses the y- axis. The x-intercept: the point at which the line crosses the x-axis.

5. Standard form of a linear equation The Standard Form of a Linear Equation is Ax+By=C, where A, B, and C are real numbers, and A and B can not both be zero.

6. Graphing equations in the standard form Steps: Set x or y to 0 to find each intercept. (Set x=0 and solve for y and then vice versa) Use the intercepts to graph the equation. (Graph each intercept and connect the dots) Ex. Graph 3x+2y=120.

7. 1 2

8. Slope Slope: the slope, is the ratio of the difference in y over the difference in x. How to calculate:

9. Slope continued… Ex. Find the slope of the line through the points (1, 6) and (4, 5)

10. Slope-intercept form The famous y=mx+b m=slope b=the y-intercept Find the slope and the y-intercept of 4x-2y=10. Then graph the line.

11. Slope-intercept form Graph y=2x-5

12. Given a point and a slope

13. Writing an equation given two points Write in slope-intercept form the equation of the line through (2,-3) and (-1, 2):

14. Properties of special slopes m=0 y is constant m is undefined x is constant mm m = m

15. Making Sense of writing equations of perpendicular lines Write the equation of the line through each point and perpendicular to a. (6, 1) b. (0,4)

16. Page 67-70 20- 30 even 38, 40, 69, 72, 74, 76, 78, 80 If you still have questions on today’s lesson visit www.PHSchool.com web code: age 0775 chapter 2, lesson 2 Homework quiz web code: aga 0202 Homework