Which equation describes the relationship between x and y?

Here are the solutions to your questions: Question 1.10 Which equation describes the relationship between x and y? Step 1: Determine the slope (m) of the linear relationship. Using the points (0, -1) and (1, 3) from the table: m = (y_2 - y_1)/(x_2 - x_1) = (3 - (-1))/(1 - 0) = (4)/(1) = 4 Step 2: Determine the y-intercept (c). From the table, when x=0, y=-1. So, the y-intercept is -1. Step 3: Write the equation in the form y = mx + c. Substitute m=4 and c=-1: y = 4x - 1 The correct option is D. D. y = 4x - 1 Question 2.1 Use prime factorisation to determine the LCM and HCF of 144 and 126. Step 1: Find the prime factorisation of 144. 144 = 2 × 72 = 2 × 2 × 36 = 2 × 2 × 2 × 18 = 2 × 2 × 2 × 2 × 9 = 2^4 × 3^2 Step 2: Find the prime factorisation of 126. 126 = 2 × 63 = 2 × 3 × 21 = 2 × 3 × 3 × 7 = 2^1 × 3^2 × 7^1 Step 3: Determine the Highest Common Factor (HCF). The HCF is the product of the common prime factors raised to the lowest power. HCF = 2^(4,1) × 3^(2,2) = 2^1 × 3^2 = 2 × 9 = 18 Step 4: Determine the Least Common Multiple (LCM). The LCM is the product of all prime factors raised to the highest power. LCM = 2^(4,1) × 3^(2,2) × 7^(0,1) = 2^4 × 3^2 × 7^1 = 16 × 9 × 7 = 144 × 7 = 1008 HCF = 18, LCM = 1008 Question 2.2.1 Simplify: 4 - 17 + 5(-2) Step 1: Perform the multiplication. 4 - 17 + (-10) Step 2: Perform the additions and subtractions from left to right. 4 - 17 - 10 = -13 - 10 = -23 -23 Question 2.2.2 Simplify: (8 + 10 - 8) × 20 ÷ 50 + 6 Step 1: Perform operations inside the parenthesis. (18 - 8) × 20 ÷ 50 + 6 10 × 20 ÷ 50 + 6 Step 2: Perform multiplication and division from left to right. 200 ÷ 50 + 6 4 + 6 Step 3: Perform the addition. 4 + 6 = 10 10 Question 2.2.3 Simplify: (-7)^3 + sqrt(49) × -6 + [3]-8 - 1^2 Step 1: Evaluate powers and roots. (-7)^3 = -343 sqrt(49) = 7 [3]-8 = -2 1^2 = 1 Step 2: Substitute these values back into the expression. -343 + 7 × -6 + (-2) - 1 Step 3: Perform the multiplication. -343 - 42 - 2 - 1 Step 4: Perform the additions and subtractions from left to right. -385 - 2 - 1 -387 - 1 = -388 -388 Question 2.3 A taxi that is transporting learners to school is travelling at an average speed of 100 km/h to cover a certain distance at 3 hours 36 minutes. At what average speed must the taxi travel to cover the same distance in 2 hours 30 minutes? Step 1: Convert the first time to hours. 3 hours 36 minutes = 3 + (36)/(60) hours = 3 + 0.6 hours = 3.6 hours Step 2: Calculate the total distance. Distance = Speed × Time = 100 km/h × 3.6 hours = 360 km Step 3: Convert the second time to hours. 2 hours 30 minutes = 2 + (30)/(60) hours = 2 + 0.5 hours = 2.5 hours Step 4: Calculate the new average speed. New Speed = DistanceNew Time = 360 km2.5 hours = 144 km/h 144 km/h Question 2.4 Lerato was 16 years of age when her parents gave her R2 800 to spend. She invested it at a bank that gave her 7.5% interest compounded annually. Now that she is 21 years of age, she wants to start a business. How much does she have in the bank? Step 1: Identify the principal amount, interest rate, and time period. Principal (P) = R2 800. Annual interest rate (i) = 7.5% = 0.075. Number of years (n) = 21 - 16 = 5 years. Step 2: Use the compound interest formula: A = P(1 + i)^n. Substitute the values into the formula. A = 2800(1 + 0.075)^5 A = 2800(1.075)^5 Step 3: Calculate the final amount. A = 2800 × 1.435629327... A ≈ 4020.00 R4020.00 Got more? Send 'em!