Question

A line passes through the points 2 -4 and 6 10 what is the equation of the line

Answer 1

We have a line passing through two points, we can employ the equation of a line in two-point form to obtain this line;

The equation is, for points

`(x_1,y_1)\&(x_2,y_2)`

The equation of a line passing through both points is;

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

For the points (2, -4) and (6, 10), we have

`\begin{gathered} (10-(-4))/(6-2)=(y-(-4))/(x-2) \\ (14)/(4)=(y+4)/(x-2) \\ \text{cross multiply, we have} \\ 4(y+4)=14(x-2)_{} \\ 4y+16=14x-28 \\ 4y=14x-16-28 \\ 4y=14x-44 \\ \text{Divide both sides by 2, to obtain} \\ 2y=7x-22 \\ y=(7)/(2)x-22 \end{gathered}`

Therefore the equation of the line is y = (7/2)x - 22