Question

What is the slope and intercept of $x-y=6$?

Answer 1

To obtain the slope and intercept of the given equation we will use the slope intercept form. Firstly we will change the given equation in slope intercept form then we will compare the equation obtained by the generalized equation to obtain our slope and $y$ -intercept. Finally we will put $y=0$ in the equation and obtain $x$ -intercept.

Complete step by step solution:
The equation given is:
$x-y=6$……$\left( 1 \right)$
The Slope intercept form is given as:
$y=mx+c$…..$\left( 2 \right)$
Where, $m=$ Slope and $c=$ $y$-intercept
So to make equation (1) in $y$-intercept form subtract $x$ on both side of the equation as:
$\begin{aligned} & x-y=6 \\\ & \Rightarrow -x+x-y=6-x \\\ & \therefore -y=6-x \\\ \end{aligned}$
Now multiply both sides by -1 and get,
$\begin{aligned} & -y=6-x \\\ & \Rightarrow \left( -1 \right)\times \left( -y \right)=\left( -1 \right)\left( 6-x \right) \\\ & \therefore y=x-6 \\\ \end{aligned}$
So the equation obtain is:
$y=x-6$
Comparing above equation by equation (2) we get,
$m=1,c=-6$
So the slope is obtained as 1 and $y$ -intercept is obtained as -6.
Next, put $y=0$ in equation (1) as:
$\begin{aligned} & x-y=6 \\\ & \Rightarrow x-0=6 \\\ & \therefore x=6 \\\ \end{aligned}$
So the $x$ -intercept is obtain as 6
Hence the slope of the equation is 1 and $x$ and $y$ intercept is -6 and 6 respectively.

Note: Linear equations are those equations whose graph is a straight line; it has only two variables which are $x$ and $y$. These equations don’t have any exponent term in them and are usually have expression as $y=mx+c$ where $c$ is the $y$ -intercept when the line is horizontal and an expression $y=m\left( x-b \right)$ where $b$ is the $x$ -intercept when the line is not horizontal. The slope intercept form is used to find the steepness of a line. It is also used for finding the slope as well as y-intercept of the line.