2-2 Linear Equations Objective: To identify equations that are linear and graph them, to write linear equations in standard form, and to determine the x- and y- intercepts of a line and use them to graph an equation. HW 2-2, pg 77, #18-36 (all) Copy problems, show work. HEADING, TITLE, OBJECTIVE!

Drill #18* Write each equation in Standard Form where A, B, and C are integers whose greatest common factor is 1. Identify A, B, and C. 1. y = -8x + 6 2. ¼ x = ½ y + 5 3. 3x – 12y = 15.

Linear Functions A function is linear if it can be defined by f(x) = mx + b, where m and b are real numbers. What is the difference between this form and standard form? What happens when the slope is 0?

Classwork #18* Identify whether the following functions are linear: 4. f(x) = 4x + 5 5. g(x) = 6 – ½ x 6. h(x) = 7. p(x) = 6

Constant Functions ** (17.) Constant Function: A function whose value does not change. (all constant functions are horizontal lines with a slope of 0) f(x) = 0 is called the zero function. What else is this line known as?

Classwork #18* Graph the following constant functions: 8. f(x) = 0 9. g(x) = -2

x and y intercepts ** 18. x – intercept: the x-coordinate of the point where the graph of a function crosses the x-axis. NOTE: At the x – intercept (on the x – axis), y = 0 19. y – intercept: the y-coordinate of the point where the graph of a function crosses the y-axis. NOTE: At the y – intercept (on the y – axis), x = 0

Finding the x- and y- intercepts You can easily graph equations by using the x- and y- intercepts. Steps: To find the x- intercept, substitute y = 0 into the equation, and solve for x To find the x- intercept, substitute y = 0 into the equation, and solve for x. Plot both points and connect. (remember to label your axes, and put arrowheads on your line.)

Example Graph 5x – 3y = 15 using x – and y – intercepts. Classwork: Graph the following: 10. x + 2y = 4 11. 2x – 3y = 6

Example 4 Page 75, Example 4.