Answer:
Step-by-step explanation: (a) y = 3x - 8 (b) 3y + x - 16 = 0
(a) The line is y = 3x - 2
But the condition for parallelism is that for two lines to be parallel to each other, their gradients m must be equal, ie, m1 = m2
therefore, the gradient of the line above m1 = 3, m2 = 3
since the line passes through the coordinate of ( 4, 4 ),
we need to find the y intersect ( c ) by substitute for x, m and y in the equation below.
y = mx + c
4 = 3 x 4 + c
4 = 12 + c
c = 4 - 12
c = -8
Therefore, substitute for c in the equation of a line above to get the second equation
y = mx + c
y = 3x - 8
(b) Condition for perpendicularity of two line is that the product of their gradients must be( -1 )
ie, m1m2 = -1
Now from the equation above, y = 3x - 2, m1 = 3 and m2 = -1/3
to get the value of c, we substitute for x, y and m into the equation
y = mx + c
4 = -1/3 x 4 = c
4 = -4/3 + c
multiply through by 3 to make it a linear equation
12 = -4 + 3c
12 + 4 = 3c
16 = 3c
c = 16/3
now put c = 16/3 into the equation , y=mx + c
y = -x/3 + 16/3
multiply through by 3
3y = -x + 16
3y + x - 16 =0
