Generally, the slope-intercept form is expressed as y = mx + b where m is the slope and b is the y-intercept of the equation. For example, if we have y = 4x - 5. 4 represents the slope and -5 is the value of the y-intercept.
The x-intercept is the value of x when y is zero and y-intercept is the value of y when x is zero.Â
Given the equation x + 3y = 6, we can rearrange the equation so that the equation is in its slope-intercept form as shown below.
[tex]y = -\frac{x}{3} + 2 [/tex]
We can assign values for x and substitute them into the equation to find the value of y as shown in the table below.
 x    y
-9 Â Â Â 5
-6 Â Â Â 4
-3 Â Â Â 3
0 Â Â Â 2
3 Â Â Â 1
6 Â Â Â 0
9 Â Â Â -1
Plotting these values into an x-y plot, we have a graph as shown in the attached image.Â
