This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Let's find the rule for the mapping by identifying the relationship between the x and y values. The given pairs (x, y) are: (-5, -5) (-3, 0) (-1, 5) (1, 10) (3, 15) (5, 20) Step 1: Find the change in x and change in y. Observe the pattern in x values: -5, -3, -1, 1, 3, 5. Each x value increases by 2. Observe the pattern in y values: -5, 0, 5, 10, 15, 20. Each y value increases by 5. Since there is a constant change, this is a linear relationship of the form y = mx + c. Step 2: Calculate the slope (m). The slope m is the ratio of the change in y to the change in x. m = (change in y) / (change in x) m = 5 / 2 Step 3: Use the slope and one point to find the y-intercept (c). Now we have the equation y = (5/2)x + c. Let's use the point (-5, -5) to find c: -5 = (5/2)(-5) + c -5 = -25/2 + c Add 25/2 to both sides: c = -5 + 25/2 c = -10/2 + 25/2 c = 15/2 Step 4: Write the complete rule for the mapping. Substitute the values of m and c into y = mx + c: y = (5/2)x + 15/2 Let's verify with another point, for example (1, 10): y = (5/2)(1) + 15/2 y = 5/2 + 15/2 y = 20/2 y = 10 This matches the given point. The rule for the mapping is: y = (5/2)x + 15/2 What's next? Send 'em! 📸