1. Olympic College Math 94 – Test on Topics 6, to 8 Math 94 – Test on Topics 6 to 8 1. 2. Find the missing value of x that makes (x, – 6) a solution to the equation: y = 2x – 8 3. (a) Determine which of the three ordered pairs does not satisfy the given equation. Equation: 2x – 3y = 9Points: (3,-2.5) (0, – 3) (– 3, – 5) -2 -3 -4 -5 -5 -4 -3 -2 -1 0 12345 x Plot each point: A(2,4), B( – 2, – 4), C(0, – 4) y 5 4 3 2 1 -2 -3 -4 -5 Page | 1 -5 -4 -3 -2 -1 0 12345 x (b) Plot the points that satisfy the equation and draw a straight line through the points: y 5 4 3 2 1

2. Page | 2 4. Graph the line y = – 3 (b) What are the coordinates of the y-intercept? (c) Write down the equation of this line. 5432154321 -5 -4 -3 -2 -1 0 12345 x Olympic College Math 94 – Test on Topics 6, to 8 y -5 -4 -3 -2 -1 0 12345 x -2 -3 -4 -5 5. Graph the line 2x – 3y = 12, using the x-intercepts and y-intercepts: y 5 4 3 2 1 -3 -4 -5 -2 2121 -5 -4 -3 -2 -1 0 12345 x -2 -3 -4 -5 6. (a) By calculating the rise and the run find the slope of this line.. y 5 4 3

3. Olympic College Math 94 – Test on Topics 6, to 8 Page | 3 7.For computer repairs, a technician charges a flat fee of $25.50, plus $20 per hour required for the repair. (a) (b) (c) Write an equation for the cost, C, she charges in terms of hours required, h. How much will it cost for a 3 hour repair? If you get $225.50 bill how many hour did the technician work for? 8.Find the slope of the line through the points (a) (– 5, – 1) and (10,6) (b) (3, – 3) and (– 3, – 3)

4. Height,h (feet) Olympic College Math 94 – Test on Topics 6, to 8 9. What is the slope and the coordinates of the y-intercept for each of the following lines. (a) y = 3x – 6 (b) 2x + 4y = 8 10. Find the equation of each line, write the equation in the form y = mx + c. 1212 (a) Slope = , through (2,– 6 ) (b) Through (–3,2) and (1,10) 11. State whether the following pairs of lines are parallel or not. (a) y – 3x = 5 and 2y + 8 = 6x (b) y = 3 and y = 2 Bonus Question 12. A hot-air balloon is rising slowly. The illustration below shows its height at 5-minute intervals for 20 minutes. (a) What is its height after 20 minutes? (b) How fast is the balloon rising every minute? 120 100 80 60 40 20 0 0510152025 Time, t (minutes) (c) Find the equation that represents the height, H, at time, t. Page | 4

5. Page | 5 Olympic College Math 94 – Test on Topics 6, to 8 Math 94 – Test on Topics 6 to 8 Solutions 1. Plot each point: A(2,4), B( – 2, – 4), C(0, – 4) 2. Find the missing value of x that makes (x, – 6) a solution to the equation: y = 2x – 8 y= 2x – 8 – 6 = 2x – 8 2=2X 1=x 3. (a) Determine which of the three ordered pairs does not satisfy the given equation. Equation: 2x – 3y = 9Points: (3,-2.5) (0, – 3) (– 3, – 5) For the point (3,-2.5) For the point (0, – 3)For the point (– 3, – 5) 2x – 3y =9 =9 =9 2(3) – 3(-2.5) =9 2(0) – 3(-3) = 9 2(-3) – 3(-5) =9 6 + 7.5 =90+9=9- 6 + 15=9 13.5=99=99=9 This point does not workThis point works -3 -4 -5 -2 -5 -4 -3 -2 -1 0 12345 x y54321y54321 A B C -2 -3 -4 -5 1 2 3 4 5 x (b) Plot the points that satisfy the equation and draw a straight line through the points: y 5 4 3 2 1

6. Rise = 7 Olympic College Math 94 – Test on Topics 6, to 8 Page | 6 4. Graph the line y = – 3 Choose x = 0 2x – 3y 2(0) – 3y 0 – 3y - 3y y ========== 12 -4 This is the point (0, - 4) Choose y = 0 2x – 3y 2x – 3(0) 2x – 0 2x x ========== 12 6 This is the point (6, 0) 6. (a) By calculating the rise and the run find the slope of this line.. Slope= 7777 =1 (b) What are the coordinates of the y-intercept? y-intercept = (0,1) (c) Write down the equation of this line.y=x+1 -2 -3 -4 -5 5. Graph the line 2x – 3y = 12, using the x-intercepts and y-intercepts: -5 -4 -3 -2 -1 0 12345 x y54321y54321 -4 -5 -2 -3 5432154321 -5 -4 -3 -2 -1 0 12345 x y -3 -4 -5 2 1 -5 -4 -3 -2 -1 0 -2 12345 x y Run = 7 5 4 3

7. Olympic College Math 94 – Test on Topics 6, to 8 Page | 7 7.For computer repairs, a technician charges a flat fee of $25.50, plus $20 per hour required for the repair. (a) (b) Write an equation for the cost, C, she charges in terms of hours required, h. C = 20h + 25.50 How much will it cost for a 3 hour repair? C = 20h + 25.50 =20(3) + 25.50=60 + 25.50=$85.50 (c)If you get $225.50 bill how many hour did the technician work for? C 225.50 200 10 ======== 20h + 25.50 20h h 8.Find the slope of the line through the points (a) (– 5, – 1) and (10,6) Slope= y 2  y 1 x 2  x 1 = 6  (  1) 10  (  5) = 7 15 (b) (3, – 3) and (– 3, – 3) Slope= y 2  y 1 x 2  x 1 =  3  (  3)  3 = 0  6 =0 9. What is the slope and the coordinates of the y-intercept for each of the following lines. Slope = 3y-intercept (0,-6) (a) y = 3x – 6 (b) 2x + 4y = 8 4y y ==== -2x + 8  2 x  8 2 y=- 0.5x + 2Slope = - 0.5y-intercept (0,2) 10. Find the equation of each line, write the equation in the form y = mx + c. 1212 (a) Slope = , through (2,– 6 ) y – y 2 = m(x – x 2 ) y – (–6) = 1212  (x – 2) y+6 y ==== 12121212  x+1 x – 5

8. Height,h (feet) Olympic College Math 94 – Test on Topics 6, to 8 10.(b) Through (–3,2) and (1,10) Slope= y 2  y 1 x 2  x 1 = 10  2 1  (  3) = 8484 =2 Slope =2, through (1,10 ) y – y 2 y – 10 y ======== m(x – x 2 ) 2(x – 1) 2x – 2 2x + 8 11. State whether the following pairs of lines are parallel or not. (a) y – 3x = 5 and 2y + 8 = 6x y = 3x + 5so its slope is 3 2y + 8 2y ==== 6x 6x – 8 y= 3x – 4 so its slope is 3, this means that these two lines are parallel. (b) y = 3 and y = 2Both are horizontal lines, this means that these two lines are parallel. Bonus Question 12. A hot-air balloon is rising slowly. The illustration below shows its height at 5-minute intervals for 20 minutes. (a) What is its height after 20 minutes? Answer = 100 feet (b) How fast is the balloon rising every minute? Answer: Increase of 40 feet in 20 minutes this is 2 feet per minute (c) Find the equation that represents the height H, at time, t. Answer H = 2t + 60 Page | 8 120 100 80 60 40 20 0 0510152025 Time, t (minutes)