2.1 Equation of a straight lineIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 2.1 Equation of a straight line

1. A line $L$ passes through the points $A(1, 4)$ and $B(5, 12)$.
   Find the equation of the line parallel to $L$ that passes through the point $(3, -1)$. Give your answer in the form $ax+by+d=0$, where $a$, $b$ and $d$ are integers.2 marks
2. The line $l_1$ has equation $3x+4y-24=0$.
   Find the coordinates of the points where $l_1$ crosses the $x$-axis and the $y$-axis.2 marks
3. A mountain road climbs from a village at a height of 420 m above sea level to a viewpoint at a height of 570 m. The horizontal distance between the village and the viewpoint is 2.5 km. The road may be modelled as a straight line.
   (i) Find the gradient of the road. (ii) Write your answer to (i) as a percentage and explain what it means for a driver.3 marks