Final answer:
To graph the line y=-3x+b, we need to find the value of b when the line passes through the point (5,2) and use the slope of -3. The graph of the line is represented by the equation y=-3x+17.
Step-by-step explanation:
To graph the line y=-3x+b, we need to find the value of b when the line passes through the point (5,2). We can use the coordinates of the point to solve for b. Since the x-coordinate is 5 and the y-coordinate is 2, we can substitute these values into the equation and solve for b.
2 = -3(5) + b
2 = -15 + b
b = 17
Now that we have the value of b, we can graph the line by plotting the point (5,2) and using the slope of -3. Starting at the point, we can move 1 unit to the right and 3 units down to find another point on the line. Connecting the two points will give us the graph of the line y=-3x+17.