9.3.7 Straight Lines, PT3 Focus Practice - Mathematics

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.

[ 5 marks ]

Solution:

(a)

\begin{array}{l} 2 y = 8 x + 3 \\ y = 4 x + \frac{3}{2} \end{array}

$\begin{array}{l} 2 y = 8 x + 3 \\ y = 4 x + \frac{3}{2} \end{array}$

m = 4

4 = 4 (6) + c

c = –2

Using formula, y = mx + c

equation of the straight line PQ is y = 4x– 20.

(b)

y = 4x – 20, at x-intercept, y = 0

4x – 20 = 0, y= 0

x = 5 or x-intercept = 5

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