Question

write the equation of a line in y = mx + b form that passes through the given pair of points (1,-2) (3,2)

Answer 1

The formula for the equation of a line given two points is,

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

Given that

`\begin{gathered} (x_1,y_1)=(1,-2) \\ (x_2,y_2)=(3,2) \end{gathered}`

Substituting the given points to the equation and expressing it in the form, y = mx+b

`\begin{gathered} (y--2)/(x-1)=(2--2)/(3-1) \\ (y+2)/(x-1)=(2+2)/(3-1) \\ (y+2)/(x-1)=(4)/(2) \\ (y+2)/(x-1)=2 \end{gathered}`

Cross multiply

`\begin{gathered} y+2=2(x-1) \\ y+2=2x-2 \\ y=2x-2-2 \\ y=2x-4 \\ \therefore y=2x-4 \end{gathered}`

Hence, the equation of a line in slope in y = mx+b is

`y=2x-4`