Final answer:
The line through the points (0,4) and (6,0) has the slope -2/3 and y-intercept 4, resulting in the equation y = (-2/3)x + 4. Multiplying by 3 to get rid of the fraction, we get the equation 2x + 3y = 12 in standard form.
Step-by-step explanation:
To find the equation of the line that passes through the points (0,4) and (6,0), we first need to determine the slope (m) of the line using the slope formula: m = (y2 - y1) / (x2 - x1). Substituting the given points into the formula yields m = (0 - 4) / (6 - 0) = -4 / 6 = -2 / 3. Since the line goes through the y-axis at (0,4), the y-intercept (b) is 4. Thus, the slope-intercept form of the line is y = mx + b or y = (-2/3)x + 4. To express this in standard form, which is Ax + By = C, we multiply every term by 3 to eliminate the fraction: 3y = -2x + 12. Rearranging terms to get x and y on one side gives us the standard form: 2x + 3y = 12. This is not one of the provided options, indicating a possible mistake in the provided options or the need to recheck our calculations.