Differentiate between the graphs of the equations $y = 3x + 1$, and $y = -3x + 1$.                [Page No. 33]

Both lines share the same $y$-intercept: when $x = 0$ both give $y = 1$, so both cross the $y$-axis at $(0, 1)$.

• $y = 3x + 1$ has slope $+3 \rightarrow$ it rises as you move right (positive slope, linear growth).

• $y = -3x + 1$ has slope $-3 \rightarrow$ it falls as you move right (negative slope, linear decay).

They are equally steep but tilt in opposite directions, so the two lines are mirror images of each other across the $y$-axis, meeting at their common point $(0, 1)$.