Question

Match the lines given on the left side with their corresponding slopes on the right..
$\begin{array}{cc}Linepassesthroughthepoints& Slopeoftheline\\ p.\left)\right(1,6\left)and\right(-4,2)& 1.)0\\ q.\left)\right(5,9\left)and\right(2,9)& 2.)-3\\ r.\left)\right(-2,-1\left)and\right(-3,2)& 3.)\frac{4}{5}\\ s.\left)\right(4,0\left)and\right(3,3)& 4.)\frac{5}{3}\end{array}$

• A. p - 3 q - 1 r - 2 s - 4
• B. p - 3 q - 1 r - 2 s - 2
• C. p - 1 q - 3 r - 1 s - 2
• D. p - 1 q - 3 r - 2 s - 2

Answer 1

The correct option is B

p - 3 q - 1 r - 2 s - 2

By definition slope of the line is $m=tan\theta$ where $\theta$ is angle made by line from +ve x-axis
If $A(x_1,y_1)$ and $B(x_2,y_2)$, where $x_1\ne x_2$ are the points on a straight line, then the slope m of the line is given by $m=\frac{y_2-y_1}{x_2-x_1}$

1. A(1,6) and B(-4,2)
Slope of AB =$\frac{2-6}{-4-1}=\frac{-4}{-5}=\frac{4}{5}$

2. A(5,9) and B(2,9)
Slope of the line =$\frac{9-9}{2-5}=\frac{0}{-3}=0$

3. A(-2,-1) and B(-3,2)
Slope of the line =$\frac{2+1}{-3+2}=\frac{3}{-1}=-3$

4. A(4,0) and B(3,3)
Slope of the line =$\frac{3-0}{3-4}=-3$