Exercises: Linear Function
If we have two points \( A(x_1,y_1) and B(x_2,y_2) \) in a straight line then

 Find the distances between these two pairs of points. Report exact answers
or accurate to 3 significant figures.
 (0,0) & (8,6)
 (1,1) & (2,1)
 (2,6) & (3,3)
 (2,5) & (3,2)
 (3,10) & (5,13)
 Find the midpoints of the line segments joining these pairs of points:
 (0,0) & (8,10)
 (3,5) & (4,10)
 (9,12) & (9,12)
 (4,4) & (2,2)
 (3,10) & (5,13)
 Find the gradient of the line joining these pairs of points:
 (0,0) & (4, 6)
 (1,0) & (2, 2)
 (3,3) & (3,3)
 (4,5) & (9,5)
 (0,0) and (0,9)
 A straight line L2 has a gradient of 2. Find the equation of line L1 that is parallel to L2 and passes through point (2,3).
 A straight line L2 has a gradient of 2. Find the equation of line L1 that is perpendicular to L2 and passes through the origin.
 L1 is a straight line that passes through (2,3) and (3,2).
 Find the equation of L1.
 L1 and L2 are perpendicular. L2 is a straight line that passes through (4,4). Find the linear equation of L2.
 L1 is a straight line passes through the origin. L1 has a gradient of 3.
L2 is a straight line that is perpendicular to L1. L2 also passes through
the origin.
 Find the gradient of L2.
 Find the linear equation of L2.
 A plane is monitored through a radar screen. The screen has Cartesian axes.
The plane moves in a straight line through points (8,2) and (2,6). The plane
also passes through the point (0,b).
 Find the gradient of the straight line joining (8,2) and (2,6).
 Find the equation of the plane's path.
 Hence or otherwise, find the value of b on the radar screen.
 The line L1 has equation \(9x + 12 y  108 =0\). L1 passes through the xaxis
at point A and passes through the yaxis at point B.
 Find the coordinates of point A and point B.
 M is the midpoint of the line segment [AB]. Find the coordinates of point M.
 Find the lengths of line segment [AB].
 L2 is a straight line that passes through the point M above and (0,6). Find the equation of L2.
 A straight line L1 passes through P(0,2) and Q(2,0). Point M is the midpoint
of line segment [PQ].
 Write down the equation of line L1 in the form of \(ax + by + c =0 \).
 A straight line L2 is perpendicular to L1 and passes through point M. Write down the equation of line L2 in the form of \(ax + by + c =0 \).
 For each of the line shown below, find its equation
 in the gradient/intercept form of \(y = mx + c\)
and  rewrite your answers above in the general form of
\(ax + by + c =0 \).
 in the gradient/intercept form of \(y = mx + c\)
Answers: (1i)10, (1ii) 3.61, (1iii) 5.83, (1iv) 8.60, (1v) 3.61
(2i) (4,5), (2ii) (3.5,2.5), (2iii) (0,0), (2iv) (1,1), (2v) (4,11.5)
(3i) 3/2, (3ii) 2/3, (3iii) 1, (3iv) 0 , (3v) undefined. This is a vertical
line.
(4) y = 2x + 7
(5) y = (1/2)x
(6)(i) y = x + 1 ; (ii) y =  x + 8
(7i) 1/3, (7ii) y =(1/3)x
(8i) slope=2/3,(8ii) y = (2/3)x + (22/3) or 3y+2x22=0
(8iii) b = 22/3 this is the yintercept
(9i) A(12,0) B(0,9), (9ii) M(6, 4.5), (9iii)15, (9iv) y = (7/4)x  6
(10i) x+y2 = 0 , (10ii) x + y = 0 or y = x.
(11) L1: y = (2/3)x and (2/3)x + y = 0
L2: y = 3x and 3x + y = 0
L3: y =x2 and x + y + 2 =0
L4: y = x+2 and x + y  2 = 0
L5: y = (3/2)x + 3 and (3/2)x + y 3 = 0
L6: y = x + 3 and x + y 3 = 0