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
Hey bilgate, good to see you again. To find the equation of the line passing through the points (2, 4) and (5, 13) in the form y = mx + c, we need to find the slope (m) and the y-intercept (c). Step 1: Calculate the slope (m). The formula for the slope is m = (y_2 - y_1)/(x_2 - x_1). Using the points (x_1, y_1) = (2, 4) and (x_2, y_2) = (5, 13): m = (13 - 4)/(5 - 2) m = (9)/(3) m = 3 Step 2: Find the y-intercept (c). Substitute the slope m=3 and one of the points (e.g., (2, 4)) into the equation y = mx + c: 4 = (3)(2) + c 4 = 6 + c c = 4 - 6 c = -2 Step 3: Write the equation of the line. Substitute the values of m and c into y = mx + c: y = 3x - 2 The equation of the line passing through the given points is y = 3x - 2. What's next?