Straight-Line Graphs: O-Level / IGCSE Maths (0580)

A straight line passes through the points $A(-2, \, 1)$ and $B(4, \, 13)$.

(a) Find the gradient of the line. [2]

(b) Write down the equation of the line in the form $y = mx + c$. [3]

(c) State the coordinates of the point where the line crosses the $y$-axis. [1]

The straight line $L$ has equation $2x + 3y = 12.$

(a) Rearrange the equation of $L$ into the form $y = mx + c$ and write down the gradient of $L$. [2]

(b) The line $P_1$ is parallel to $L$ and passes through the point $A(6,\,1)$. Find the equation of $P_1$, giving your answer in the form $y = mx + c$. [2]

(c) The line $P_2$ is perpendicular to $L$ and also passes through the point $A(6,\,1)$. Find the equation of $P_2$, giving your answer in the form $ax + by = c$, where $a$, $b$ and $c$ are integers. [3]

The straight line $L$ passes through the points $P(0,\,5)$ and $Q(4,\,-1)$. Find the equation of $L$ in the form $y = mx + c$.

A rainwater tank is being emptied through an outlet. The volume of water $V$ litres remaining in the tank after $t$ minutes lies on a straight line. When $t = 2$ the tank holds $630$ litres, and when $t = 6$ it holds $450$ litres.

(a) Find the gradient of the line through the points $(2,\,630)$ and $(6,\,450)$. [2]

(b) Find the equation of the line in the form $V = mt + c$. [2]

(c) Write down the volume of water in the tank at the moment the outlet was opened, and state what the gradient tells you about how the tank is emptying. [2]

(d) A second tank drains at the same rate but starts full with $900$ litres at $t = 0$. Write down the equation of the line for the second tank, and hence work out how long it takes this tank to empty completely. [3]