5.7 SPM Practice (Long Questions 2)

Question 3:
Diagram below shows a straight line JK and a straight line ST drawn on a Cartesian plane. JK is parallel to ST.


Find
(a) the equation of the straight ST,
(b) the x-intercept of the straight line ST.

Solution:
(a) 
JK is parallel to ST, therefore gradient of JK = gradient of ST.
= 8 0 0 4 = 2
Substitute m = –2 and S (5, 6) into y = mx + c
6 = –2 (5) + c
c = 16
Therefore equation of ST: y = –2x + 16

(b)

For x-intercept, y = 0
0 = –2x + 16
2x = 16
x = 8
Therefore x-intercept of ST = 8



Question 4:


In the diagram above, PQRS is a parallelogram. Find
(a)  the gradient of SR,
(b) the equation of QR,
(c)  the x-intercept of QR.

Solution:
(a)
PQ is parallel to SR, gradient of PQ = gradient of SR.
Gradient of SR= 6 3 =2

(b)
Gradient of QR= 86 50 = 2 5 Substitute m= 2 5  and R (5,8) into y=mx+c 8= 2 5 ( 5 )+c c=6 Therefore equation of QR: y= 2 5 x+6

(c)
For x-intercept, y = 0 0 = 2 5 x + 6 x = 15
Therefore x-intercept of QR = –15.