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;

$\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}$

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

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

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