Straight Lines

Question 13: Diagram shows a straight line ST and a straight line PQ drawn on a Cartesian plane.  ST is  parallel to PQ. Given that equation of the straight line ST is 2y = 8x + 3.    Find, (a)  the equation of the straight line PQ, (b)  the x-intercept of the straight line PQ. … Read more

Question 11: Diagram 11 shows two parallel straight lines, POQ and RMS drawn on a Cartesian plane. Diagram 11 Find (a) the equation of the straight line RMS, (b) the x-intercept of the straight line MN. Solution: (a) m RMS = m POQ        = 1−0 −2−0        =− 1 2 At point ( 4, 6 ) y 1 =m x 1 +c 6=− … Read more

Question 9: The diagram above shows that the straight line PMQ intersects with PNR at N. Given that OQ = OR and M is the midpoint of PQ. Find (a) the coordinate of P (b) the value of m and n. Solution: (a) Given M is midpoint of PQ x-coordinate of P=0 For y-coordinate of P, y+0 2 =3 y=6 Coordinates of P=( 0,6 ). (b) 0+4 … Read more

Question 7: The diagram above shows a parallelogram on a Cartesian plane. MP and NO are parallel to the y-axis. Given that the distance of MZ is 4 units. Find (a) the value of p and q. (b) the equation of the straight line MN. Solution: (a) Line NO is parallel to y-axis, p=2 MP= 3 2 + 4 2 … Read more

Question 5:   In the diagram above, a straight line 5x + 7y + 35 = 0 intersects with the x-axis and y-axis at R and S respectively. Determine (a) the gradient of the straight line RS. (b) the x-intercept of the straight line RS. (c) the distance of RS.   Solution: (a) 5 x … Read more

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 … Read more

Question 1: In diagram below, ABCD is a trapezium drawn on a Cartesian plane. BC is parallel to AD and O is the origin. The equation of the straight line BC is 3y = kx+ 7 and the equation of the straight line AD is y = 1 2 x + 3 Find (a) the value of k, (b) the x-intercept … Read more

(A) Equation of Parallel Lines   To find the equation of the straight line which passes through a given point and parallel to another straight line, follow the steps below:   Step 1 : Let the equation of the straight line take the form y = mx + c. Step 2 : Find the gradient of the … Read more

9.2.1 Parallel Lines   (A) Gradient of parallel lines 1. Two straight lines are  parallel if they have the same gradient. If PQ // RS, then mPQ = mRS     2. If two straight lines have  the same gradient, then   they are parallel.  If mAB = mCD then AB // CD Example 1: Determine whether the two straight lines are parallel. (a) 2y – 4x … Read more

9.1.1 Equation of a Straight Line: y = mx + c 1. Given the value of the gradient, m, and the y-intercept, c, an equation of a straight line y = mx + c can be formed. 2. If the equation of a straight line is written in the form y = mx + c, the gradient, m, … Read more