1. Today’s Topics: Writing Equations of Lines Parallel/Perpendicular Average Rate of Change Today’s Topics: Writing Equations of Lines Parallel/Perpendicular Average Rate of Change

2. General Form of the Equation of a Line The general form of the equation of a line is ax + by = c, where a, b, and c are real numbers, with a and b not both equal to 0.

3. Forms of Linear Equations General formax + by = cwhere a, b, and c are real numbers, with a and b not both equal to 0. Point-slope y – y 1 = m(x – x 1 )where m is the form slope of the line and (x 1, y 1 ) is a point on the line.

4. Forms of Linear Equations Slope-intercept y = mx + bwhere m is the formslope of the line and b is the y-intercept. Vertical linex = awhere a is a constant, and a is the x-coordinate of any point on the line. The slope is undefined. Horizontal liney = bwhere b is a constant, and b is the y-coordinate of any point on the line. The slope is 0.

6. D. Write the equation for the line that pass through the point (-1, 5) and has a slope of zero in slope-intercept form. C. Write the equation of the line with slope of 4 and y-intercept of - 2 in point-slope form.

7. 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. A.Write an equation for the amount of Internet advertising spending as a function of the number of years after 2009. B.Use the function to estimate the amount that will be spent on internet advertising in 2015.

8. Parallel Lines have the __SAME__ slope. Perpendicular Lines have slopes that are __NEGATIVE_ _RECIPROCAL__ of each other. Parallel Lines have the __SAME__ slope. Perpendicular Lines have slopes that are __NEGATIVE_ _RECIPROCAL__ of each other. A.Write the equation of the line through (4, 5) and parallel to the line with the equation 7x - 2y = -1. B.Write the equation of the line through (2, -3) and perpendicular to the line with the equation 2x + 3y -6 = 0.

9. 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

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

11. Difference Quotient The average rate of change of the function f(x) from x to x + h is

12. For the function f(x) = x 2 + 1, whose graph is shown, find f(x + h). Difference Quotient