Final answer:
The correct answer is option b) 5x + 4y = 20.The standard form of the equation for the line that passes through the points (0,5) and (4,0) is 5x + 4y = 20, which is option b.
Step-by-step explanation:
To find the standard form of the equation of a line that passes through two points, we can use the formula for the slope (m) given by Δy/Δx, where Δ denotes the difference between the corresponding coordinates of the points. The slope is calculated as (0 - 5) / (4 - 0) = -5/4. Using the point-slope form of a line's equation, (y - y1) = m(x - x1), and substituting one of the points (such as (0,5)) and the slope, we get (y - 5) = -5/4(x - 0). Multiplying each side by 4 to clear the fraction gives us 4y - 20 = -5x. Rearranging to get the standard form Ax + By = C, we have 5x + 4y = 20.
To determine the standard form of the equation of a line, we need to find the slope and y-intercept.
Using the slope formula, we find the slope (m) to be -5/4. Then, substituting one of the given points (0, 5) into the point-slope form, we can solve for the y-intercept (b). Finally, rearranging the equation to the standard form, we obtain 5x + 4y = 20.