need to find intercepts and graph 3x+y=6

To find the intercept form, arrange the equation to match the general form \[y = \text{a}\: x + \text{b} \]

to get the x-intercept, set the variable y to 0. to get the y-intercept, set the variable x to 0. when you have the intercepts, plot the coordinates.

first perform it as normal function you got used to. we will get y=6-3x when function can intersect y-axes? when x is set to 0. therefore you have to plug in x=0 in original function/ you will get :6-3*0=6. So when x=0 y=6 and at this point your graph intersects y-axes. Now graph will intersect x-axes when y is set to 0. therefore we will get: 6-3x=0. Solve this equation. -3x=-6 x=2 so point where your graph has intersection with x-axes is (2:0)

Here is the graph of the function \[y=-3x+6\] or \[y=6-3x\] which ever you prefer

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