Question

How do you find the slope and intercept to graph $2x+y=7$?

Answer 1

The equation given in the question must first be converted to the standard slope intercept form of a line. For this, we need to subtract $2x$ from the given equation $2x+y=7$ for separating $y$ in terms of $x$. Then, comparing the obtained equation with the standard slope intercept form of a line, which is given by $y=mx+c$, we will obtain the slope and the intercept of the graph corresponding to the given equation.

Complete step by step answer:
The equation given in the question is written as
$2x+y=7........(i)$
The graph of the given equation will look like

For determining the slope and the intercept of the given equation, we need to write it in the form of the standard slope intercept form of a line. We know that the slope intercept form of the equation of a line is given by
$y=mx+c.........(ii)$
From the above equation, we can see that only the variable $y$ is present in the left hand side, while the term containing the variable $x$ is written on the right hand side along with all the other constants.
For this, we subtract $2x$ from both the sides of the equation (i) to get
$\begin{aligned} & \Rightarrow 2x+y-2x=7-2x \\\ & \Rightarrow y=7-2x \\\ \end{aligned}$
Writing the above equation in the form of the equation (ii), we get
$\Rightarrow y=-2x+7........(iii)$
By comparing the equations (ii) and (iii), we get the slope and the intercept of the line as
$\Rightarrow m=-2,c=7$

Hence, the slope of the graph $2x+y=7$ is equal to $-2$ and its intercept is equal to $7$.

Note: We can also solve this question by writing the equation of line in the standard form of $px+qy+r=0$. So the given equation $2x+y=7$ is to be written as $2x+y-7=0$ so that we will get $p=2$, $q=1$ and $r=-7$. The slope is equal to the negative of the ratio of the coefficient of $x$ to the coefficient of $y$, that is, $m=-\dfrac{p}{q}$. And the intercept is given by $c=-\dfrac{r}{q}$.