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
To work out the gradient of the lines, we use the formula: m = (y_2 - y_1)/(x_2 - x_1) a) For the first line: Step 1: Identify two clear points on the line. We can see the line passes through (-3, 0) and (2, -3). Let (x_1, y_1) = (-3, 0) and (x_2, y_2) = (2, -3). Step 2: Substitute the coordinates into the gradient formula. m_a = (-3 - 0)/(2 - (-3)) Step 3: Calculate the gradient. m_a = (-3)/(2 + 3) = (-3)/(5) The gradient of line (a) is -(3)/(5). b) For the second line: Step 1: Identify two clear points on the line. We can see the line passes through (0, -3) and (6, 6). Let (x_1, y_1) = (0, -3) and (x_2, y_2) = (6, 6). Step 2: Substitute the coordinates into the gradient formula. m_b = (6 - (-3))/(6 - 0) Step 3: Calculate the gradient. m_b = (6 + 3)/(6) = (9)/(6) Step 4: Simplify the fraction. m_b = (3)/(2) The gradient of line (b) is (3)/(2). Send me the next one 📸