MAT 150– Algebra Class #4 Today’s Topics: Writing Equations of Lines Parallel/Perpendicular Average Rate of Change MAT 150– Algebra Class #4

Forms of Linear Equations Description General Where a, b and c are real numbers, With a and b not both equal to 0. Point-Slope Where m is the slope of the line and (x1, y1) is a point on the line. Slope-Intercept Where m is the slope of the line and b is the y-intercept. Vertical Line Where a is a constant and a is the x-coordinate of any point on the line. The slope is undefined. Horizontal Where b is a constant and b is the y-coordinate of any point on the line. The slope is 0.

Writing the Equation of a Line Write an equation for the line that passes through the point (-1, -5) and has slope 3 4 . Write an equation for the line that passes through the points (-1, 3) and (2, 6). Write an equation for the line that pass through the point (-1, 5) and has a slope of zero. What would the equation be if the slope was undefined? Write the equation of the line with slope of 4 and y-intercept of -2.

Equations in Real-Life Internet Advertising The amount spent on Internet advertising was $22.7 billion in 2009 and is expected to grow at a rate of $2.25 billion per year for the next five years. Write an equation for the amount of Internet advertising spending as a function of the number of years after 2009. Use the function to estimate the amount that will be spent on internet advertising in 2015.

Ex 3: Parallel and Perpendicular Lines Parallel Lines have the __SAME__ slope. Perpendicular Lines have slopes that are __NEGATIVE_ _RECIPROCAL__ of each other. Write the equation of the line through (4, 5) and parallel to the line with the equation 7x - 2y = -1. Write the equation of the line through (2, -3) and perpendicular to the line with the equation 2x + 3y = 6.

The average rate of change between two points on its graph is the slope of the line joining the two point. Such a line is called a secant line. Average Rate of Change The average rate of change of f(x) with respect to x over the interval from x = a to x = b (where a < b) is calculated as 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒= 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑓 𝑥 𝑣𝑎𝑙𝑢𝑒𝑠 𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑𝑖𝑛𝑔 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 𝑣𝑎𝑙𝑢𝑒𝑠 = 𝑓 𝑏 −𝑓 𝑎 𝑏 −𝑎

Average Rate of Change For the function shown in the figure, find the average rate of change from point B to point A.

𝑓 𝑥+ℎ −𝑓 𝑥 (𝑥+ℎ) −𝑥 = f x+h −f x h Different Quotient Difference Quotient The average rate of change of the function f(x) from x to x+h is 𝑓 𝑥+ℎ −𝑓 𝑥 (𝑥+ℎ) −𝑥 = f x+h −f x h For the function 𝑓 𝑥 = 2𝑥 2 +1, find 𝑓 𝑥+ℎ −𝑓 𝑥 ℎ .

Assignment Page 69-72 #1-21 odd #26-27 #33 #36