Final answer:
The standard form of the line that passes through the points (0,4) and (7,0) is 4x + 7y = 28.
Step-by-step explanation:
The standard form of the line that passes through the points (0,4) and (7,0) can be found using the point-slope form of a linear equation, which is y - y1 = m(x - x1). First, we need to find the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (0 - 4) / (7 - 0) = -4/7. Now we can substitute the value of m and one of the given points into the point-slope form to get the standard form: y - 4 = (-4/7)(x - 0). Simplifying, we get y - 4 = -4/7x. Finally, let's rearrange the equation in the standard form Ax + By = C, where A, B, and C are integers and A is positive. Multiplying both sides of the equation by 7, we get 7y - 28 = -4x. Rearranging, we have 4x + 7y = 28. Therefore, the standard form of the line is 4x + 7y = 28.