Answer:
The graph of 6x+3y=18 is straight line graph .
Step-by-step explanation:
Given : 6x+3y=18
Solution :
[tex]6x+3y=18[/tex]
[tex]y = \frac{18-6x}{3}[/tex]
[tex]y= 6 - 2x [/tex] ----(a)
The general form of equation of line is y = mx+c
comparing general form with equation (a)
We can see equation (a) is in the form of general form of equation of line
where m = -2 (slope)
So, this equation has a straight line graph.
We can also check by finding and plotting the points on the graph
[tex]y= 6 - 2x [/tex]
For x = 0 in this equation we get the value of y = 6-(2*0) = 6-0 = 6
(0,6) is the coordinate of this equation .
Take another value of x i.e. x= 1 then y will be : y = 6-(2*1) = 6-2 = 4
(1,4) is the coordinate of this equation .
Again with another value of x i.e. x= 2 then y will be : y = 6 - (2*2) = 6 - 4 = 2
(2,2) is the coordinate of this equation .
Again with another value of x i.e. x=3 then y will be : y = 6 - (2*3) = 6 - 6 = 0
(3,0) is the coordinate of this equation .
Plotting these points we are getting a straight line graph (refer to attached file )
Thus, the given equation is a straight line graph .
