Mathematics Assignment

1
Mathematics Assignment
Student Name:
Instructor Name:
Course Number:
1st May 2019

2
Assignment 5 Questions
Q1.a) For two perpendicular lines the product of their gradients equals to negative one.
i.e. M1M2=-1 where M1 and M2 are the gradients
of line 1and line 2 respectively.
- 1
3M2= -1 , M2= 3
𝑦 − 0
𝑥 + 2
3
= 3
𝑦 = 3(𝑥 + 2
3)
y= 3x+2
The perpendicular line to y=− 1
3x +1 and passing
(− 2
3 ,0) has the equation y= 3x+2.
y-3x=2
Dividing through by 2 we have 𝑦
2 - 3
2x=1
𝑦
2 + 𝑥
−2
3
=1
X-intercept =− 𝟐
𝟑 , y-intercept=2
b) Gradient of straight line passing through
(1,-1) and (-1,-2) is
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 = Δ𝑦
Δ𝑥 = −2+1
−1−1 =−1
−2= 1
2
For two perpendicular lines the product of their
gradients equals to negative one.
i.e. M1M2=-1 where M1 and M2 are the gradients
of line 1 and line 2 respectively.

3
1
2M2= -1 , M2= -2
𝑦 − 1
𝑥−0 = −2 ,
y-1=-2(x-0)
y-1=-2x
y=-2x +1
𝑦
1 + 𝑥
−1
2
=1
X-intercept =− 𝟏
𝟐 , y-intercept=1
c) Two or more lines are parallel if they have the same gradient.
y=2x+2
The gradient of line 2= The gradient of line 1 = 2
𝑦 − 1
𝑥 + 1
2
= 2
y-1=2(𝑥 + 1
2 )
y-1=2x+1
y=2x+2
y-2x=2
𝑦
2 + 𝑥
−1=1
X-intercept =−𝟏 , y-intercept=2
d) The gradient through (-1,0) and (1,-2)
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 = Δ𝑦
Δ𝑥 = 0+2
−1−1 = 2
−2= −1
The gradient of line 1= The gradient of line 2 = -1
𝑦 − 1
𝑥 − 0 = −1
y-1= -x
y= -x +1

4
y+x =1
𝑦
1 + 𝑥
1=1
X-intercept =𝟏, y-intercept=1
Q 2a) y=3x-1
3M2= -1 , M2= - 1
3
𝑦 − 1
𝑥−3 =- 1
3
3(y-1)= -1(x-3)
3y-3=-x+3
3y= -x+6
𝑦
2 + 𝑥
6=1
x-intercept =6, y-intercept=2
b) 𝑦+1
𝑥−1
2
=- 2
y+1= -2 (𝑥 − 1
2 )
y+1=-2x+1
y=- 2x
x-intercept =0, y-intercept=0
c) The gradient through (-1,-3) and (2,0)
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 = Δ𝑦
Δ𝑥 = 0+3
2+1 =3
3= 1
1M2 = −1 , M2 = −1
𝑦 − 4
𝑥−1 = -1
y-4= - 1(x-1)
y-4= -x +1
y= -x+5