Graphing Equations Chapter Test Review Part 1: Calculate the slope of the following lines: (Lesson 3) Unit 2: Graphing Equations 2. Find the slope of a line that has a 3. Find the slope of the line that y-intercept of -4 and contains the point (3, -2) contains the following points: (-5, 4) (2, -4)
Part 2: Graphing Slope and Slope Intercept Form (Lessons 4 and 5) 4. Write the equation for the line represented on the graph: Unit 2: Graphing Equations 5. Graph the following equations on the grid: a. y = -3x+ 2 b. y = 1/3 x 8
Part 3: Finding Slope Given Two Points and Rate of Change (Lessons 6 & 7) 6. Find the slope of the line that contains the following points: (-6, 9)(-4, -4) Unit 2: Graphing Equations 7. A line has a y-intercept of 8 and passes through the point (-2, -9). Without graphing the line, determine the slope of the line. 8. In Jessica s first year in her career, she made $39000. In her sixth year, she makes $52500. What is Jessica s average rate of change over her six years in her career. 9. Jesse is investing money in the stock market. His initial investment when he opened the account was $50. By the end of January he had gained $250. By the end of February he had lost $150. At the end of March he remained steady with no gains or losses. By the end of April he gained $440. a. Create a graph to show the total amounts in Jesse s account each month.
b. What was Jesse s total amount at the end of April? c. What was the rate of change between his initial deposit and his amount at the end of April? d. What was the rate of change between February and march? Explain how you determined your answer. Part 4: Graphing Standard Form Equations (Lessons 8 & 9) 10. Identify the x and y intercepts for the following equation: 4x 3y = 24 11. Write an equation that is equivalent to each of the following equations: a. 6x + 2y = -14 2. 3x 2y = -12 12. Graph the following equations: a. 2x + 4y = -16 b. -6x 4y = -24
13. Mel is ordering t-shirts for the lacrosse team. Short sleeve t-shirts cost $10 and long sleeve t- shirts cost $17. The total bill came to $293.00. The equation that represents x short sleeve t-shirts and y long sleeve t-shirts is: 10x+17y = 293 Graph the equation on the grid. Let x = the number of short sleeve t-shirts y = the number of long sleeve t-shirts If 14 people ordered short sleeve t-shirts, how many long sleeve t-shirts were ordered? Justify your answer mathematically. Part 5: Graphing Absolute Value Equations 1. y= x+2 2. y= - x+2-1 Identify two solutions.
Graphing Equations Chapter Test Review Answer Key Part 1: Calculate the slope of the following lines: (Lesson 3) Unit 2: Graphing Equations Slope = rise Slope = 10 = 5 Run 4 2 The slope is 5/2. Slope = rise Slope = -6 = - 3 Run 2 The slope is -3. 2. Find the slope of a line that has a 3. Find the slope of the line that y-intercept of -4 and contains the point (3, -2) contains the following points: (-5, 4) (2, -4) Slope = rise Slope = 2 Run 3 The slope of this line is 2/3. Slope = rise Slope = 8 Run -7 The slope of this line is -8/7.
Part 2: Graphing Slope and Slope Intercept Form (Lessons 4 and 5) 4. Write the equation for the line represented on the graph: Unit 2: Graphing Equations y-int To write the equation in slope intercept form, we need to know the slope and y-intercept. Y = mx +b Slope (m) = -1 Y-int (b) = -2 Y = -x - 2 5. Graph the following equations on the grid: To write the equation in slope intercept form, we need to know the slope and y-intercept. Y = mx +b Slope (m) = 1/2 Y-int (b) = 4 Y = 1/2x + 4 a. y = -3x+ 2 b. y = 1/3 x 8 We can start by plotting the y-intercept which is y = 2. From that point, graph the slope. Slope is a rise of -3 and run of 1. We can start by plotting the y-intercept which is y = -8. From that point, graph the slope. Slope is a rise of 1 and run of 3.
Part 3: Finding Slope Given Two Points and Rate of Change (Lessons 6 & 7) 6. Find the slope of the line that contains the following points: (-6, 9)(-4, -4) Use the slope formula to calculate the slope when given two points. y 2 y 1-4 9 = -13 or -6.5 x 2 - x 1-4 (-6) 2 The slope of the line is: -13/2 or -6.5 Unit 2: Graphing Equations 7. A line has a y-intercept of 8 and passes through the point (-2, -9). Without graphing the line, determine the slope of the line. In order to determine the slope of the line, we must have two points. We know one point is (-2,-9) and we know the y-intercept is 8. The y-intercept can also be written as (0,8) because the y- intercept is the point on the y-axis, so we know the x-coordinate is 0. Now we have two points. (0,8) (-2,-9) Now we can use the slope formula to find the slope. y 2 y 1 = -9-8 = -17 or 8.5 x 2 - x 1-2 0-2 The slope of the line is 17/2 or 8.5 8. In Jessica s first year in her career, she made $39000. In her sixth year, she makes $52500. What is Jessica s average rate of change over her six years in her career. If we write two ordered pairs for this problem, then we can determine the rate of change, which is also the slope. Therefore, we can use the slope formula. Let x = the number of years & y = her salary First year - $39000 can be written as: (1, 39000) Sixth year - $52500 can be written as: (6, 52500) Now we can use the slope formula to determine the rate of change. y 2 y 1 = 52500 39000 = 13500 = 2700 x 2 - x 1 6-1 5 Jessica s rate of change is $2700 per year.
9. Jesse is investing money in the stock market. His initial investment when he opened the account was $50. By the end of January he had gained $250. By the end of February he had lost $150. At the end of March he remained steady with no gains or losses. By the end of April he gained $440. a. Create a graph to show the total amounts in Jesse s account each month. b. What was Jesse s total amount at the end of April? At the end of April Jesse s total was $590. (50+250-150+0+440 = 590) c. What was the rate of change between his initial deposit and his amount at the end of April? Let s write two ordered pairs for this information. Initial Deposit(month 0) - $50 is (0, 50) April (4 th month) 590 is (4, 590) Let x = the month Let y = the total amount) Now we can use our slope formula to find the rate of change. y 2 y 1 = 590 50 = 540 = 135 x 2 - x 1 4-0 4 The rate of change between the initial deposit and the end of April is $135. d. What was the rate of change between February and March? Explain how you determined your answer. The rate of change between February and March is 0. The problem states that at the end of March is account remained steady with no gains or losses. The ordered pairs would be: (2, 150) (3, 150)
Part 4: Graphing Standard Form Equations (Lessons 8 & 9) 10. Identify the x and y intercepts for the following equation: 4x 3y = 24 To identify the x intercept, we will let y = 0 To identify the y-intercept, we will let x = 0 4x 3(0) = 24 4x = 24 Substitute 0 for y Simplify 4(0) 3y = 24 Substitute 0 for x -3y = 24 Simplify 4x/4 = 24/4 Divide by 4 X = 6 The x-intercept is 6. -3y/-3 = 24/-3 Divide by -3 Y = -8 The y-intercept is -8 11. Write an equation that is equivalent to each of the following equations: a. 6x + 2y = -14 2. 3x 2y = -12 I need to write an equation in slope intercept form in order for the equation to be equivalent. Therefore, we will solve for y. I need to write an equation in slope intercept form in order for the equation to be equivalent. Therefore, we will solve for y. 6x 6x + 2y = -14 6x Subtract 6x 3x 3x 2y = - 12 3x Subtract 3x 2y = -6x 14 Simplify -2y = -3x 12 Simplify 2y/2 = -6x/2-14/2 Divide by 2 Y = -3x 7 Y = -3x 7 is an equivalent equation. -2y/-2 = -3x/-2 12/-2 Divide by -2 Y = 3/2x + 6 Y = 3/2x + 6 is an equivalent equation.
12. Graph the following equations: a. 2x + 4y = -16 b. -6x 4y = -24 Since this equation is written in standard form, you can find the x and y intercepts. (You may also rewrite it in slope intercept form). We will find the intercepts. Since this equation is written in standard form, you can find the x and y intercepts. (You may also rewrite it in slope intercept form). We will find the intercepts. X-intercept (Let y = 0) Y-int (Let x=0) X-intercept (Let y = 0) Y-int (Let x=0) 2x +4(0) = -16 2(0) +4y = -16 2x = -16 4y = -16 2x/2 = -16/2 4y/4=-16/4 X = -8 Y = -4 **If you rewrote the equation in slope intercept form, it would be: Y = -1/2x 4-6x 4(0) = -24-6(0) 4y = -24-6x = -24-4y = -24-6x/-6 = -24/-6-4y/-4 = -24/-4 X = 4 y = 6 **If you rewrote the equation in slope intercept form, it would be: Y = -3/2 + 6
13. Mel is ordering t-shirts for the lacrosse team. Short sleeve t-shirts cost $10 and long sleeve t- shirts cost $17. The total bill came to $293.00. The equation that represents x short sleeve t-shirts and y long sleeve t-shirts is: 10x+17y = 293 Graph the equation on the grid. Let x = the number of short sleeve t-shirts y = the number of long sleeve t-shirts Since this equation is written in standard form, I can find the x and y intercepts in order to graph. Since we are dealing with larger numbers, this is definitely the easiest way to graph this equation. 10x + 17y = 293 X int: (Let y = 0) Y int: (Let x = 0) 10x + 17(0) = 293 10(0) + 17y = 293 10x = 293 17y = 293 10x/10 = 293/10 17y/17 = 293/17 X = 29.3 y = 17.2 If 14 people ordered short sleeve t-shirts, how many long sleeve t-shirts were ordered? Justify your answer mathematically. According to the graph, if 14 people ordered short sleeve t-shirts, then 9 long sleeve t-shirts were ordered. Justify: 10(14) + 17(9) = 293 140 + 153 = 293 293= 293
Part 5: Graphing Absolute Value Equations and Inequalities 1. y= x+2 2. y = - x+2-1 Identify two solutions. Two solutions are: (-5, -4) and (-4, -3) **Graphs and table of values were created using a free calculator on rentcalculators.org**