Find the equation of the line which is parallel to the line \(5 x+4 y=9\) and makes an intercept of 4 units on the \(x\)-axis.
A. \(5 x-4 y=9\) B. \(5 y+4 x=20\) C. \(5 y-5 x=20\) D. \(4 y+5 x\) \(=20\)
Correct Answer: D
Explanation
Since the required line is parallel to \(5 x+4 y=9\). they must therefore have the same gradient.xpressing \(5 x+4 y=9\) in the form \(y=m x+c\) where \(m\) is the gradient \begin{array}{l} \Rightarrow 5 x+4 y=9 \\ 4 y=-5 x+9 \\ y=-\frac{5 x}{4}+\frac{9}{4} \\ m=-\frac{5}{4} \end{array} for the required line. let its equation be \(y=m x+c\). where \(m\) also equals \(-5 / 4\) \(c=\) intercept on the \(y\)-axis thus. \(y=-\frac{5}{4} x+c\) if the line makes an intercept of 4 units on the \(x\)-axis. then \(x=4, y=0\) substituting \(0=-\frac{5}{4}(4)+c\) \(0=-5+c \cdot c=5\) and finally \(y=-\frac{5}{4} x+5\) Multiply through by 4 . \(4 y=-5 x+20\) \(4 y+5 x=20\) \(4 y+5 x=20\)