Final answer:
The equation of a line through the points (0,9) and (3,0) is y = -3x + 9.
Step-by-step explanation:
The equation of a line through the points (0,9) and (3,0) can be found using the slope-intercept form of a linear equation, which is given by y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. Plugging in the values, we get m = (0 - 9) / (3 - 0) = -9 / 3 = -3. Now that we have the slope, we can use one of the points, such as (0,9), and the slope to find the y-intercept. Plugging in the values into the equation y = mx + b and solving for b, we get 9 = -3(0) + b, which simplifies to b = 9. Therefore, the equation of the line is y = -3x + 9. So the correct answer is A) y = -3x + 9.