Question

What is an equation of the line that passes through the pints (1, 1) and (7, -5)?

Answer 1

Given the a line passes through points (1, 1) and ( 7, -5) i.e

`\begin{gathered} (x_1,y_1)\Rightarrow(1,1) \\ (x_2,y_2)\Rightarrow(7,-5) \end{gathered}`

The formula to find the equation of a straight line is

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

Substitute the values into the formula above

`\begin{gathered} (y-y_1)/(x-x_1)=(y_2-y_1)/(x_2-x_1) \\ (y-1)/(x-1)=(-5-1)/(7-1) \end{gathered}`

Solve for y

`\begin{gathered} (y-1)/(x-1)=(-5-1)/(7-1) \\ (y-1)/(x-1)=(-6)/(6) \\ (y-1)/(x-1)=(-1)/(1) \\ \text{Crossmultiply} \\ 1(y-1)=-1(x-1) \\ y-1=-x+1 \\ y=-x+1+1 \\ y=-x+2 \end{gathered}`

Hence, the equation of the line is

`y=-x+2`