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
Step 1: Find the slope of the given line. The given line is 8x + 7y = 5. To find its slope, convert it to the slope-intercept form y = mx + b. 8x + 7y = 5 \\ 7y = -8x + 5 \\ y = -(8)/(7)x + (5)/(7) The slope of the given line is m = -(8)/(7). Step 2: Determine the slope of the new line. Since the new line is parallel to the given line, it will have the same slope. So, the slope of the new line is m_new = -(8)/(7). Step 3: Use the point-slope form to find the equation of the new line. The new line passes through the point (x_1, y_1) = (7, -14) and has a slope m_new = -(8)/(7). The point-slope form is y - y_1 = m(x - x_1). y - (-14) = -(8)/(7)(x - 7) \\ y + 14 = -(8)/(7)(x - 7) Step 4: Convert the equation to slope-intercept form (y = mx + b) and simplify. Distribute the slope on the right side: y + 14 = -(8)/(7)x + (-(8)/(7))(-7) \\ y + 14 = -(8)/(7)x + 8 Subtract 14 from both sides to isolate y: y = -(8)/(7)x + 8 - 14 \\ y = -(8)/(7)x - 6 The equation of the line is y = -(8)/(7)x - 6. Last free one today — make it count tomorrow, or type /upgrade for unlimited.