Introduction to Graphs

Positive $x$ puts it to the right of the $y$-axis\; negative $y$ puts it below the $x$-axis. Right and below is the fourth quadrant.

The equation is already in the form $y = mx + c$, so $m = -3$ and $c = 4$. The negative gradient means the line falls as you move right.

$m = \dfrac{-4 - 5}{2 - (-1)} = \dfrac{-9}{3} = -3$. Subtracting a negative on the bottom gives $2 + 1 = 3$.

Substituting $x = 3$ gives $y = 4(3) - 5 = 7$, not 8. The point on the line at $x = 3$ is $(3, 7)$, so $(3, 8)$ sits one unit above it.

Start from $y = -2x + c$. Substituting $(4,1)$ gives $1 = -8 + c$, so $c = 9$. Check: $-2(4) + 9 = 1$ ✓

Set $x = 0$ for the $y$-intercept: $y = -12$. Set $y = 0$ for the $x$-intercept: $3x = 12$, so $x = 4$.