Determine whether each equation is a linear equation. Write yes or no. If yes, write the equation in standard form. y = 4x + 3 Rewrite the equation in standard form. The equation is now in standard form where A = 4, B = 1, and C = 3. The equation is linear. x 2 + 3y = 8 Because x is squared, the equation cannot be written in standard form. The equation is not linear. Rewrite the equation in standard form. The equation is now in standard form where A = 1, B = 3, and C = 4. The equation is linear. esolutions Manual - Powered by Cognero Page 1
Graph each equation using the x and yintercepts. y = 3x 6 To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them. To find the x-intercept, let y = 0. To find the y-intercept, let x = 0. So, the x-intercept is 2 and the y-intercept is 6. 2 + 5 = 10 esolutions Manual - Powered by Cognero Page 2
2x + 5y = 10 To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them. To find the x-intercept, let y = 0. To find the y-intercept, let x = 0. So, the x-intercept is 5 and the y-intercept is 2. esolutions Manual - Powered by Cognero Page 3
Graph each equation by making a table. y = 2x To make the table of values, start at x = 0 and evaluate y. Continue this process for other values of x. Plot the points and draw a line through them. x y points 2 4 (2, 4) 1 2 (1, 2) 0 0 (0, 0) 1 2 (1, 2) 2 4 (2, 4) x = 8 y To make the table of values, start at x = 0 and evaluate y. Continue this process for other values of x. Plot the points and draw a line through them. x y points 2 10 (2, 10) 1 9 (1, 9) 0 8 (0, 8) 1 7 (1, 7) 2 6 (2, 6) esolutions Manual - Powered by Cognero Page 4
BOOK SALES The equation 5x + 12y = 240 describes the total amount of money collected when selling x paperback books at $5 per book and y hardback books at $12 per book. Graph the equation using the x- and y- intercepts. To graph the equation, find the x- and y-intercepts. Plot these two points. Then draw a line through them. To find the x-intercept, let y = 0. To find the y-intercept, let x = 0. So, the x-intercept is 48 and the y-intercept is 20. esolutions Manual - Powered by Cognero Page 5
Find the root of each equation. x + 8 = 0 The root, or solution, of an equation is any value that makes the equation true. So, the root is 8. 4x 24 = 0 The root, or solution, of an equation is any value that makes the equation true. So, the root is 6. 18 + 8x = 0 The root, or solution, of an equation is any value that makes the equation true. So, the root is. esolutions Manual - Powered by Cognero Page 6
The root, or solution, of an equation is any value that makes the equation true. So, the root is. Solve each equation by graphing. 5x + 35 = 0 The related function is y = 5x + 35. The graph intersects the x-axis at 7. So, the solution is 7. 14 84 = 0 esolutions Manual - Powered by Cognero Page 7
14x 84 = 0 The related function is y = 14x 84. The graph intersects the x-axis at 6. So, the solution is 6. 118 + 11x = 3 The related function is y = 11x + 121. The graph intersects the x-axis at 11. So, the solution is 11. esolutions Manual - Powered by Cognero Page 8
MULTIPLE CHOICE The function y = 15 + 3x represents the outside temperature, in degrees Fahrenheit, in a small Alaskan town where x represents the number of hours after midnight. The function is accurate for x values representing midnight through 4:00 p.m. Find the zero of this function. 0 3 5 15 The zero is located at the x-intercept of the function. To find the x-intercept, let y = 0. The zero is 5. The correct choice is C. Find the rate of change represented in the table. To find the rate of change, use the coordinates (1, 2) and (4, 6). So, the rate of change is. esolutions Manual - Powered by Cognero Page 9
Find the slope of the line that passes through each pair of points. (2, 6), (4, 12) So, the slope is 3. (1, 5), (3, 8) So, the slope is. (3, 4), (2, 6) So, the slope is 2. esolutions Manual - Powered by Cognero Page 10
So, the slope is. esolutions Manual - Powered by Cognero Page 11
MULTIPLE CHOICE Find the value of r so the line that passes through the pair of points has the given slope. (4, 8), (r, 12), m = 4 1 0 3 The correct choice is G. Find the slope of the line that passes through the pair of points. So, the slope is 12. esolutions Manual - Powered by Cognero Page 12
POPULATION GROWTH The graph shows the population growth in Heckertsville since 2003. a. For which time period is the rate of change the greatest? b. Explain the meaning of the slope from 2003 to 2009. a. Looking at the graph, the slope is the steepest from 20062007, so the rate of change for that period is the greatest. b. The population changed from about 16,000 to about 19,700 from 2003 to 2009. Find the slope. So, the average rate of change in population is about 630. This means that there was an average increase of about 630 people per year in Heckertsville between 2003 and 2009. esolutions Manual - Powered by Cognero Page 13