Question 15047
I'm not familiar with the THEA guide book, but when you are graphing an equation like 2x + 3y = 6, I can't imagine why you would want to solve for x.  Solving for y is a nice idea, but I don't think that is the easiest way to graph this equation.


Nevertheless, solve for y by adding -2x from both sides:
2x + 3y = 6
2x-2x + 3y = -2x + 6
3y = -2x + 6


Next, divide both sides by 3 in order to solve for y.
3y= -2x + 6
{{{(3y)/3 = (-2x)/3 + 6/3}}}
{{{y = -2x/3 + 2}}}


What this means is the the y intercept is 2, and the slope (steepness!) of the line is -2/3.


Start with an xy graph, and go up two units on the y-axis and put a point.  Next, with your pencil on this point on the y axis, measure off the slope which is a rise of -2 followed by a run of 3.  This means from the point you made at y=2 on the y-axis, count DOWN 2 units, and go RIGHT 3 units, and put another point.  Then connect the points with a line, and extend the line in both directions. The result should look like this:

{{{graph (300, 300, -10, 10, -10, 10, (-2/3)*x + 2)  }}}


R^2 at SCC