Question

Draw the graph of $2x+y=8.$

Answer 1

Hint: To draw the graph of \[2x+y=8\], first we will find the value of ‘y’ then we will take ‘x’ as $0,1,2,3,4.........$ to find the x and y coordinates. At last we will plot the points on a graph and join the points to get a graph.

Complete step by step solution:
Here, in this question we are asked to draw the graph of $2x+y=8$ .So, we will find the coordinates of the points where this line intersects x-axis and y-axis. Now, we will solve the given equation to get the value of ‘y’.
The equation given in the question is –
$2x+y=8$
By subtracting $2x$ on both sides, we get –
$y=8-2x$
By arranging the terms, we get –
$y=-2x+8$
The equation we get is in slope-intercept in the form of $y=mx+b$.
Where, $m=-2$ and $b=8$ .
So, to get x and y coordinates as to graph this equation,
Let us consider ‘x’ as $0,1,2,3,4..........$
If we take $x=0$
Then, we get $y=-2x+8$
$\begin{align}
  & y=-2\left( 0 \right)+8 \\
 & y=-0+8 \\
 & y=8 \\
\end{align}$
So, the coordinate be $\left( 0,8 \right)$
If we take $x=1$
Then, we get $y=-2x+8$
$\begin{align}
  & y=-2\left( 1 \right)+8 \\
 & y=-2+8 \\
 & y=6 \\
\end{align}$
So, the coordinate be $\left( 1,6 \right)$
If we take $x=2$
Then, we have $y=-2x+8$
$\begin{align}
  & y=-2\left( 2 \right)+8 \\
 & y=-4+8 \\
 & y=4 \\
\end{align}$
So, the coordinate be $\left( 2,4 \right)$
If we take $x=3$
Then, we get $y=-2x+8$
$\begin{align}
  & y=-2\left( 3 \right)+8 \\
 & y=-6+8 \\
 & y=2 \\
\end{align}$
So, the coordinate be $\left( 3,2 \right)$
If we take $x=4$
Then, we get $y=-2x+8$
$\begin{align}
  & y=-2\left( 4 \right)+8 \\
 & y=-8+8 \\
 & y=0 \\
\end{align}$
So, the coordinate be $\left( 4,0 \right)$
So, the $\left( x,y \right)$ coordinates are $\left( 0,8 \right),\left( 1,6 \right),\left( 2,4 \right),\left( 3,2 \right),\left( 4,0 \right).....$
By plotting these coordinates on x-axis and y-axis of graph, we get –

Hence, the straight line drawn above is the graph of the equation of $2x+y=8$ .

Note: Generally students get confused while finding x & y coordinates. They can find it also in other way
The y-intercepts is the value of ‘y’ when $x=0$ .
In this case $y=-2x+8$ where -2 is the slope and the y intercepts is 8. Based on y-intercepts we know that one point on the line is at $\left( x,y \right)=\left( 0,8 \right)$
The slope $\left( -2 \right)$ tells us that for every unit increment $\left( i.e.+1 \right)$ of the x value, the y value changes by $\left( -2 \right)$ . So, we can build a table of a few sample points.

X	Y	$\left( x,y \right)$
0	8	$\left( 0,8 \right)$
1	$\left( 8-2 \right)=6$	$\left( 1,6 \right)$
2	$\left( 6-2 \right)=4$	$\left( 2,4 \right)$
3	$\left( 4-2 \right)=2$	$\left( 3,2 \right)$
4	$\left( 2-2 \right)=0$	$\left( 4,0 \right)$ .