Question

Find the equation of the line in standard form that passes through the following points. Eliminate any fractions and simplify your answer

Answer 1

Answer:

7x-10y=57

Explanation:

The following two points are on a line:

$\begin{gathered} (x_1,y_1)=(-9,-12) \\ (x_2,y_2)=(1,-5) \end{gathered}$

To find the equation of the line, use the two-point formula for the equation of a line.

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

Substitute the given points:

$\frac{y-(-12)}{x-(-9)}=\frac{-5-(-12)}{1-(-9)}$

Then simplify:

$\begin{gathered} \frac{y+12}{x+9}=\frac{-5+12}{1+9} \\ \frac{y+12}{x+9}=\frac{7}{10} \end{gathered}$

Cross multiply:

$10(y+12)=7(x+9)$

Open the bracket:

$\begin{gathered} 10y+120=7x+63 \\ 7x-10y=120-63 \\ 7x-10y=57 \end{gathered}$

The equation of the line is 7x-10y=57.