Question

How do you write an equation of a line with point $\left(1,5\right)$ slope $-1$?

Answer 1

Finding the equation of the line.

Given, a line with a slope $-1$passes through point $\left(1,5\right)$.

The point-slope formula for the equation of the line is :

$y-y_1=m\left(x-x_1\right)$.

Where, $m$ is the slope of the line and $\left(x_1,y_1\right)$is the point through which the line passes.

Putting the values of $m$ as $-1$and $\left(x_1,y_1\right)$as $\left(1,5\right)$ in the equation of the line.

$\begin{array}{rcl}y-5& =& -1\left(x-1\right)\\ & \Rightarrow & y-5=1-x\\ & \Rightarrow & y=-x+6\end{array}$,

Hence, the equation of the line with point $\left(1,5\right)$ slope $\mathbf{-}\mathbf{1}$ is $\mathit{y}\mathbf{=}\mathbf{-}\mathit{x}\mathbf{+}\mathbf{6}$.