Question

How do you graph the equation $x + y = - 6$ and find the $y$ intercept?

Answer 1

We will plot the graph for the equation of lines using intercept form of equation. We will find the intersection points of line on the graph. The intersection point will satisfy the equation of line. We have to find the intercepts of the line on $x -$ axis and $y -$ axis. To find the $y -$ intercept of line, substitute $x = 0$ in the equation of line and substitute $y = 0$ in the equation of line to get $x -$ intercept of the line. We can also find the intercept of the line with an alternative method. We will equate the equation of a given line with the equation of the general form of line. The general equation of a line having slope of $m$ and intercepts on the coordinate axis $c$ is $y = mx + c$. Slope is denoted by $m$.

Complete step by step solution:
Step: 1 the given equation of the line is,
$x + y = - 6$
To graph the line, first find the intercepts made by the line on the axis.
To find the $y -$ intercept of the line, substitute $x = 0$ in the given equation of line,
$\Rightarrow x + y = - 6 \\\ \Rightarrow 0 + y = - 6 \\\ \Rightarrow y = - 6 \\\$
So the $y -$intercept of the line is $\left( {0, - 6} \right)$,
Step: 2 to find the $x -$intercept of the line, substitute $y = 0$ in the equation of the given line.
$\Rightarrow x + y = - 6 \\\ \Rightarrow x + 0 = - 6 \\\ \Rightarrow x = - 6 \\\$
So the $x -$intercept of the line is $\left( { - 6,0} \right)$.
Now compare the equation of line with general equation of line $y = mx + c$ and find the slope of the line.$\Rightarrow m = - 1$
Now plot the points $\left( { - 6,0} \right)$ and $\left( {0, - 6} \right)$ on the graph and connect them by drawing a straight line.

**
Therefore the $y -$ intercept of the line is $\left( {0, - 6} \right)$ and the graph is plotted.**

Note:
Plot the equation of line on the graph by finding its intercept made by them on the axis. To find the intercept made by lines on the axis, substitute $x = 0$ and $y = 0$ in the equation of lines. Students are advised to remember the equation of standard line $y = mx + c$ where $m$ is the slope of line and $c$ is the $y -$ intercept of line.