Question

Write the standard form of the equation of the line through the pair of points (-7,5) and (-9,10). write the equation using only integer coefficients

Answer 1

The general equation of line with the pair of coordinates are express as:

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

From the given data we have :

$\begin{gathered} (x_1,y_1)=(-7,5) \\ (x_2,y_2)=(-9,10) \end{gathered}$

Substitute them on the equation of the line and simplify :

$\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-5=\frac{10-5}{(-9)-(-7)}(x-(-7)) \\ y-5=\frac{5}{-9+7}(x+7) \\ y-5=\frac{5}{-2}(x+7) \\ (-2)(y-5)=5(x+7) \\ -2y+10=5x\text{ + 35} \\ 5x\text{ + 2y +35-10=0} \\ 5x+2y+25=0 \end{gathered}$

Equation of line is 5x + 2y + 25 = 0

Answer : 5x + 2y + 25 = 0