The equation of a line in the slope intercept form is expressed as
y = mx + c
The given equation is
9x + 3y = 18
We would rearrange it so that it takes the form of the slope intercept equation shown above.
We would divide both sides of the equation by 3, we have
9x/3 + 3y/3 = 18/3
3x + y = 6
Subtracting 3x from both sides of the equation, we have
3x - 3x + y = 6 - 3x
y = 6 - 3x
The slope intercept form is
y = - 3x + 6
To plot the graph, we would substitute values of x into the equation to get corresponding y values. These x and y values would be plotted on the x and y coordinates of the graph. We have
For x = - 2, y = 6 - 3(- 2) = 6 + 6 = 12
For x = - 1, y = 6 - 3(-1) = 6 + 3 = 9
For x = 0, y = 6 - 3(0) = 6 - 0 = 6
For x = 1, y = 6 - 3(1) = 6 - 3 = 3
For x = 2, y = 6 - 3(2) = 6 -6 = 0
The graph is shown below