Differentiate between the graphs of the equations y = 3x + 1, and y = –3x + 1.

Both equations are of the form y = ax + b.

To draw the graph, we identify suitable points on each line.

Equation 1 : y = 3x + 1

x = 1, y = 4

x = 2, y = 7

x = -1, y = -2

Equation 2 : y = –3x + 1

x = 0, y = 1

x = 2, y = -5

x = -2, y = 7

Similarities:

Both lines have the same y-intercept, b = 1, so both lines cut the y-axis at the same point (0, 1).

Differences:

The line y = 3x + 1 has a positive slope (a = 3), so it rises from the bottom-left to the top-right of the coordinate plane. It represents linear growth.

The line y = -3x + 1 has a negative slope (a = -3), so it falls from the top-left to the bottom-right of the coordinate plane. It represents linear decay.

Hence, the two lines pass through the same point (0, 1) on the y-axis but have slopes opposite in sign, so one rises and the other falls.