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To graph the equation y = 4x + 3 by hand choose any two values of x. For example x = 1 gives y = 7 and x = 0 gives y = 3. The graph of the equation is a straight line drawn between the points (0, 3) and (1, 7)

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y = 4x + 3 is in what is called "slope-intercept" form or "y=mx+b" form which is the easiest form for graphing.  The "3" is called the "y-intercept" and is where the line crosses the y axis.  So, go to the "origin" (0,0) and go up three on the vertical line.  Place a point there.  This is one of the points on the line.  Next, we look at the number in front of the "x."  This is the "slope" or "rise over run."  Since we do not have a fraction, we can put a "1" under the "4" to make a fraction.  So, our slope is 4/1.  We go from our (0,3) over 1 to 1 and up 4 to 7.  So, another point on the line is (1,7).  You only need two points to make a line so connect the points and continue off the graph in both directions.  Don't forget the arrows at both ends to indicate that the line continues in both directions to infinity.

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It is not possible to solve the equation y = 4x + 3. This is merely a relation between two variables x and y. The variable y is 3 greater than 4 times the variable x.

Only if the value of either of the variables is fixed the other can be determined so that the two meet the given criterion.

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