Question

What is the equation of the line that passes through the points (7,2) and (-2,-5)

Answer 1

Given: Two points below:

`\begin{gathered} (7,2) \\ (-2,-5) \end{gathered}`

To Determine: The equation of the line passing through the given line

The formula for finding the equation of the line passing through two given points is

`\begin{gathered} (x_1,y_1);(x_2,y_2) \\ \text{equation formula} \\ (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \end{gathered}`

Use the formula to find the equation of the given points as shown below:

`\begin{gathered} (7,2);(-2,-5) \\ x_1=7;y_1=2 \\ x_2=-2;y_2=-5 \\ By\text{ substitution into the formula} \\ (y-2)/(x-7)=(-5-2)/(-2-7) \end{gathered}`
`\begin{gathered} (y-2)/(x-7)=(-7)/(-9) \\ (y-2)/(x-7)=(7)/(9) \\ \text{cross}-\text{multiply} \\ 9(y-2)=7(x-7) \end{gathered}`
`\begin{gathered} 9y-18=7x-49 \\ 9y-7x=-49+18 \\ 9y-7x=-31 \end{gathered}`

Hence, the equation of the line passing through the points (7,2) and (-2,-5) is

9y-7x=-31