Page Even 14. Yes 4x – y = No 18. Yes 4x – y = , , 4

CFU Analyze the characteristics of graphs of basic linear relations and linear functions including constant function, direct variation, identity function, vertical lines, absolute value of linear functions CLE Use technology where appropriate SPI Solve problems involving linear equations and linear inequalities.; Write and/or solve linear equations, inequalities, and compound inequalities including those containing absolute value. SPI Determine the equation of a line and/or graph a linear equation. Objective: To be able to solve a linear equation by graphing

A.linear; y = 2x – 9 B.linear; 2x + y = –9 C.linear; 2x + y + 9 = 0 D.not linear Determine whether y = –2x – 9 is a linear equation. If it is, write the equation in standard form.

Graph y = –3x + 3. A.B. C.D.

Linear Functions  Root – any value that makes the equation true  Replace zero with f(x)

Solution for Linear Equation 2x -8 = 0 Algebraically 2x = 8 x = 4 Solve Graphically f(x) = 2x – 8 or y=2x -8 4 is the x intercept 4 is the root of 2x-8 4 is the zero of f(x) = 2x - 8

Solve an Equation with One Root Answer: So, the solution is –3. The graph intersects the x-axis at –3. The related function is To graph the function, make a table.

A.x = 4;B.x = –4; C.x = –3;D.x = 3;

Solve 2x + 5 = 2x + 3. Answer: Since f(x) is always equal to 2, this function has no solution. 2x + 2 = 2xSubtract 3 from each side. 2x + 5 = 2x + 3Original equation 2 = 0Subtract 2x from each side. The related function is f(x) = 2. The root of the linear equation is the value of x when f(x) = 0. Method 1 Solve algebraically.

Solve 5x – 7 = 5x + 2. Answer: Therefore, there is no solution. 5x – 9 = 5xSubtract 2 from each side. 5x – 7 = 5x + 2Original equation –9 = 0Subtract 5x from each side. Graph the related function, which is f(x) = –9. The graph of the line does not intersect the x-axis. Method 2 Solve graphically.

Estimate by Graphing FUNDRAISING Kendra’s class is selling greeting cards to raise money for new soccer equipment. They paid $115 for the cards, and they are selling each card for $1.75. The function y = 1.75x – 115 represents their profit y for selling x greeting cards. Find the zero of this function. Describe what this value means in this context. The graph appears to intersect the x-axis at about 65. Solve algebraically to check. Make a table of values.

Estimate by Graphing Answer: The zero of this function is about Since part of a greeting card cannot be sold, they must sell 66 greeting cards to make a profit. 0 = 1.75x – 115Replace y with 0. y = 1.75x – 115Original equation 115 = 1.75xAdd 115 to each side ≈ xDivide each side by 1.75.

Practice Assignment  Page odd

Page odd No solution /7 17. No solution 19. No solution 21. No solution / / /