Graph -x+3y=6

Problem

−x+3*y=6

Solution

1. Identify the equation as a linear equation in two variables, which represents a straight line.

2. Solve for y to put the equation into slope-intercept form, y=m*x+b where m is the slope and b is the y-intercept.

3. Add x to both sides of the equation.

3*y=x+6

4. Divide every term by 3 to isolate y

y=1/3*x+2

5. Determine the y-intercept by looking at the constant term. The y-intercept is (0,2)

6. Determine the slope by looking at the coefficient of x The slope is m=1/3 meaning the line rises 1 unit for every 3 units it moves to the right.

7. Find the x-intercept by setting y=0 in the original equation.

−x+3*(0)=6

−x=6

x=−6

8. Plot the points (−6,0) and (0,2) on a coordinate plane and draw a straight line through them to complete the graph.

Final Answer

y=1/3*x+2

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