Question

How do you find the slope and intercept of $y=-x-7$?

Answer 1

In this problem we need to calculate the slope and intercept of the given line $y=-x-7$. We know that slope is the ratio of variation in $y$ for unit variation in $x$. So, we will calculate the values of $y$ where $x=0$, $x=1$ by substituting those values in the given equation and simplifying them. Now we will take the difference between the values of $y$ and we will consider this as the slope of the given equation. Now we will take the value of $y$ whereas the intercept of the given equation.

Complete step by step answer:
Given the equation, $y=-x-7$.
Substituting the value of $x=0$ in the above equation, then we will get
$\begin{aligned} & y=-0-7 \\\ & \Rightarrow y=-7 \\\ \end{aligned}$
Substituting the value of $x=1$ in the above equation, then we will get
$\begin{aligned} & y=-1-7 \\\ & \Rightarrow y=-8 \\\ \end{aligned}$
Now the slope of the given equation is the variation of the $y$ for unit variation in $x$. Mathematically we can write it as
$m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$
Substituting the above calculated values in this equation, then we will get
$\begin{aligned} & m=\dfrac{-8-\left( -7 \right)}{1-0} \\\ & \Rightarrow m=-8+7 \\\ & \Rightarrow m=-1 \\\ \end{aligned}$
Hence the slope of the given equation is $m=-1$.
Now the intercept of the given line is the value of $y$ where $x=0$. We have already calculated the value of $y$ where $x=0$ which is nothing but $y=-7$.
Hence the intercept of the given equation is $c=-7$.

Note:
In this problem we have calculated the slope and intercept by calculating the values of $y$. We can also calculate the slope and intercept without calculating the values of $y$. We have the slope intercept form of a line as $y=mx+c$ where $m$ is the slope of the line and $c$ is the $y$- intercept. So, we will compare the given equation with $y=mx+c$, then we will get
$m=-1$, $c=-7$
From both the methods we got the same result.