Question 579434: How do you solve and graph this? Please HELP!!
y-3=3(x-2) and y=6x-12
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Linear equations graph as straight lines. All you need is two good points for each line. Choosing your points is an art, and you get better with practice.
The equation  is expressed in a form known as the point-slope form.
The slope of a line passing through point (2,3) and point (x,y) would be calculates as
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So is the equation of a line that passes through (2,3) and has a slope of 3.
You can plot the point (2,3) to start.
Since the slope is increase in y (rise) divided by increase in x (run), starting from (2,3) you could run 1 space to the right and rise 3 spaces up to mark a second point for the line.
 Then you connect the points with a straight line. 
The equation  is given in slope intercept form.
The coefficient of x, 6, is the slope and the constant -12 is the y-intercept, the y coordinate of the point where the line crosses the y-axis that is the line where x=0.
That gives you point (0,-12) to start. Using the slope to run 1 unit right and rise 6 up from (0,-12) you would get to (1,-6) and repeating the running and rising, you would get to points (2,0) and (3,6).
You can use any pair of those points to draw the second line, but I'd pick (2,0) and (3,6) because they fit in the graph I started before. And then I would connect them with a straight line.
 AT this point you may realize that the lines intersect at (3,60.
The point (3,6) represents the solution to the system of linear equations: x=3 paired with y=6.
It is good to verify by substituting those values in the equations, especially if the intersection is not one of your carefully calculated points.
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