Question

if P(t-1,t t+1) and Q(2t, 3t) are two points, then the slope of the line will be negative if a) t<-2, b) t>1/2, c) -2 =-2

Answer 1

Answer:

when $t<2$, the slope will be negative.

Step-by-step explanation:

The slope $m$ of a line passing through two points $(x,y)$ and $(a,b)$ is,

$m=\dfrac{b-y}{a-x}$

Given that the line passing through the points $P(t-1,t+1)$ and $Q(2t,3t)$. So the slope is,

$m=\dfrac{3t-(t+1)}{2t-(t-1)} =\dfrac{3t-t-1}{2t-t+1}=\dfrac{2t-1}{t+1}$

So we can check for what values of $t$ the slope is negative.

$m<0 \\\\\implies \dfrac{2t-1}{t+1}<0 \\\\\implies 2t-1<t+1\\\\\implies 2t-t<1+1\\\\\implies t<2$

So when $t$ less than 2, the slope will be negative.