Question

Find an equation for the line that passes through the points (-1,5) and (-5,1)

Answer 1

x-y=-6

Step-by-step explanation:

Given the points (-1,5) and (-5,1)​:

To find the equation of the line, we use the two-point formula:

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

Substitute these points into the formula:

`(y-5)/(x-(-1))=\frac{1-5}{-5_{}-(-1)}`

Then simplify:

`\begin{gathered} (y-5)/(x+1)=\frac{1-5}{-5_{}+1} \\ (y-5)/(x+1)=(-4)/(-4) \\ (y-5)/(x+1)=1 \\ y-5=x+1 \\ -5-1=x-y \\ x-y=-6 \end{gathered}`

The equation of the line is:

`x-y=-6`