Question: Show that all line through the points A (p, p +1) and B (2p, p +2) with p ≠ 0 cross the negative x-axis

How do I have to do this?

Guest Aug 20, 2015

#1**+5 **

A (p, p +1) and B (2p, p +2)

$$\\gradient=\frac{p+2-p-1}{2p-p}\\\\

gradient=\frac{1}{p}\\\\

y=\frac{x}{p}+b\\\\

Sub\;in\;point\;A\\\\

p+1=\frac{p}{p}+b\\\\

p+1=1+b\\\\

so\;b=p\\\\

$Equation of line is $ y=\frac{x}{p}+p\\\\$$

If p is negative the the y intercept is negative and the gradient is negative so it will cut the negative x axis.

If p is positive the the y intercept is positive and the gradient is positive so it will cut the negative x axis.

Melody
Aug 20, 2015