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?
+118609 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.
