 ## 5.7.3 The Straight Line, SPM Paper 2

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   = 9+16   = 25 … Read more

## 5.7.2 The Straight Line, SPM Paper 2

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= 8−6 5−0 = 2 5 Substitute m= 2 5  and R (5,8) into y=mx+c 8= 2 … Read more

## 5.7.1 The Straight Line, SPM Paper 2

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

## 5.6.2 The Straight Line, SPM Paper 1 (Short Questions)

5.6.2 The Straight Line, SPM Paper 1 (Short Questions) Question 6: Diagram below shows a straight line RS with equation 3y = –px – 12, where p is a constant.   It is given that OR: OS = 3 : 2. Find the value of p. Solution: Method 1: Substitute x= –6 and y = … Read more

## 5.6.1 The Straight Line, SPM Paper 1 (Short Questions)

Question 1: Diagram below shows a straight line RS on a Cartesian plane.   Find the gradient of RS. Solution: Using gradient formula  y 2 − y 1 x 2 − x 1 Gradient of RS= 3−1 5−( −1 ) = 2 6 = 1 3 Question 2: In diagram below, PQ is a straight line with gradient  − … Read more

## 5.5.1 Parallel Lines (Sample Questions)

Example 1: The straight lines MN and PQ in the diagram above are parallel. Find the value of q. Solution: If two lines are parallel, their gradients are equal. m1 = m2 mMN = mPQ using gradient formula y 2 − y 1 x 2 − x 1 9 − 4 5 − ( − … Read more

## 5.5 Parallel Lines

5.5 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

## 5.4.1 Equation of a Straight Line (Sample Questions)

Example 1: Given that the equation of a straight line is 4x + 6y – 3 = 0. What is the gradient of the line? Solution: 4x + 6y – 3 = 0 6y  = – 4x + 3 y = − 4 x 6 + 3 6 y = − 2 3 x + 1 2 … Read more

## 5.4 Equation of a Straight Line

5.4 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

## 5.3.1 Intercepts (Sample Questions)

Example 1: The x-intercept of the line ST is Solution: The x-coordinate for the point of intersection of the straight line with x-axis is -0.4. Therefore the x-intercept of the line ST is –0.4. Example 2: Find the x-intercept of the straight line 2x + 3y + 6 = 0. Solution: 2x + 3y + 6 … Read more