Question

1. Find the equation of the line that passes through the points (1, -2) and (4,7).

Answer 1

The general form of equation of line passing through two points is :

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

we have :

`(x_1,y_1)=(1,-2)(x_2,y_2)\text{ =(4,7)}`

Substitute these value in the genral form of line:

`\begin{gathered} y-(-2)=(7-(-2))/(4-1)(x-1) \\ y+2=(7+2)/(3)(x-1) \\ y+2=(9)/(3)(x-1) \\ y+2=3(x-1) \\ y+2=3x-3 \\ 3x-y=2+3 \\ 3x-y=5 \\ 3x-y-5=0 \\ \text{Solve the equation in terms of y} \\ y=3x-5 \end{gathered}`

The required equation of line : y = 3x - 5

Answer: D) y = 3x - 5