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

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.

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

Substitute the given points:

`(y-(-12))/(x-(-9))=(-5-(-12))/(1-(-9))`

Then simplify:

`\begin{gathered} (y+12)/(x+9)=(-5+12)/(1+9) \\ (y+12)/(x+9)=(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.