Question

Find the equation in terms of x of the line passing through the points

Answer 1

Given:

The points of the line are,

`\begin{gathered} (x_1,y_1)=(-3,-2) \\ (x_2,y_2)=(1,5) \end{gathered}`

The objective is to find the equation of the line in terms of x.

Step-by-step explanation:

The general equation of a straight line using two points is,

`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)\text{ . . . .(1)}`

On plugging the given values in equation (1),

`(y-(-2))/(5-(-2))=(x-(-3))/(1-(-3))`

On further solving the above equation,

`\begin{gathered} (y+2)/(5+2)=(x+3)/(1+3) \\ (y+2)/(7)=(x+3)/(4) \\ 4(y+2)=7(x+3) \\ 4y+8=7x+21 \\ 4y=7x+21-8 \\ 4y=7x+13 \\ y=(7)/(4)x+(13)/(4) \end{gathered}`

Hence, the equation of the line in terms of x is y = (7x/4)+(13/4).