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
You're on a roll — Step 1: Calculate the gradient (slope) of the line. The given points are (x_1, y_1) = (-4, 0) and (x_2, y_2) = (8, 9). The formula for the gradient m is: m = (y_2 - y_1)/(x_2 - x_1) Substitute the coordinates: m = (9 - 0)/(8 - (-4)) m = (9)/(8 + 4) m = (9)/(12) m = (3)/(4) Step 2: Find the equation of the line using the point-slope form. Using the point (-4, 0) and the gradient m = (3)/(4): y - y_1 = m(x - x_1) y - 0 = (3)/(4)(x - (-4)) y = (3)/(4)(x + 4) Multiply both sides by 4 to eliminate the fraction: 4y = 3(x + 4) 4y = 3x + 12 Step 3: Convert the equation to the intercept form (x)/(a) + (y)/(b) = 1. Rearrange the equation 4y = 3x + 12 to have the constant term on one side: 3x - 4y = -12 To get 1 on the right side, divide the entire equation by -12: (3x)/(-12) - (4y)/(-12) = (-12)/(-12) Simplify the fractions: (x)/(-4) + (y)/(3) = 1 Comparing this to (x)/(a) + (y)/(b) = 1, we have a = -4 and b = 3. The equation of the straight line in the required form is (x)/(-4) + (y)/(3) = 1. What's next?