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

Thanks!

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.