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
Here are the solutions for finding the gradient and y-intercept for each equation. The general form of a linear equation is y = mx + c, where m is the gradient and c is the y-intercept. a) y = 3x - 2 Step 1: The equation is already in the form y = mx + c. Step 2: Identify the gradient and y-intercept. The gradient is m = 3. The y-intercept is c = -2. Gradient: 3 Y-intercept: -2 b) y = 2x + 4 = 0 Assuming the intended equation is y = 2x + 4. Step 1: The equation is already in the form y = mx + c. Step 2: Identify the gradient and y-intercept. The gradient is m = 2. The y-intercept is c = 4. Gradient: 2 Y-intercept: 4 c) x + y = 0 Step 1: Rearrange the equation into y = mx + c form. x + y = 0 y = -x y = -1x + 0 Step 2: Identify the gradient and y-intercept. The gradient is m = -1. The y-intercept is c = 0. Gradient: -1 Y-intercept: 0 d) y = -3x + 6 Step 1: The equation is already in the form y = mx + c. Step 2: Identify the gradient and y-intercept. The gradient is m = -3. The y-intercept is c = 6. Gradient: -3 Y-intercept: 6 e) x - y = 0 Step 1: Rearrange the equation into y = mx + c form. x - y = 0 x = y y = x y = 1x + 0 Step 2: Identify the gradient and y-intercept. The gradient is m = 1. The y-intercept is c = 0. Gradient: 1 Y-intercept: 0 f) 3x + y = 2 Step 1: Rearrange the equation into y = mx + c form. 3x + y = 2 y = -3x + 2 Step 2: Identify the gradient and y-intercept. The gradient is m = -3. The y-intercept is c = 2. Gradient: -3 Y-intercept: 2 g) x - y = 2 Step 1: Rearrange the equation into y = mx + c form. x - y = 2 -y = -x + 2 y = x - 2 y = 1x - 2 Step 2: Identify the gradient and y-intercept. The gradient is m = 1. The y-intercept is c = -2. Gradient: 1 Y-intercept: -2 h) y - (2x - 2) Assuming the intended equation is y = 2x - 2. Step 1: The equation is already in the form y = mx + c. Step 2: Identify the gradient and y-intercept. The gradient is m = 2. The y-intercept is c = -2. Gradient: 2 Y-intercept: -2 3 done, 2 left today. You're making progress.