Question

Graph the line y = -3x + b if it is known that the graph goes through point (1,3). What is the value of b?

A) b = 6
B) b = 4
C) b = 3
D) b = -6

Answer 1

By substituting the given point (1,3) into the equation y = -3x + b, we find the value of b is 6, which corresponds to option A. The slope of the line indicates that it will slope downward to the right.

Step-by-step explanation:

To determine the value of b in the equation y = -3x + b, we can use the given point (1,3) through which the line passes. Substituting x = 1 and y = 3 into the equation:

3 = -3(1) + b

Adding 3 to both sides gives us:

3 + 3 = b

Thus, b = 6. The correct value of b is 6, which corresponds to option A.

If we are to graph the line, we would plot point (1,3) and use the slope m = -3, which indicates that for every one unit increase in x, y decreases by 3 units. This slope means the line will slope downward to the right, as shown in Figure 12.4 part (c).