Question 22034
If the equation is given in the form y = mx + b, then the constant term, which is b, is the y intercept, and the coefficient of x, which is m, is the slope of the straight line.


The easiest way to graph such a line, is to plot the y-intercept first.  Then, write the slope m in the form of a fraction, like rise over run, and from the y-intercept, count up (or down) for the rise, over (right or left) for the run, and put the next point.  Then connect the two points and this is your line.  


A couple of examples might be helpful.  


EXAMPLE 1:  y = 3x + 2

SOLUTION:
Y-intercept = 2, slope = {{{3/1 = (rise)/(run) }}}

Start by graphing the y-intercept by going up 2 units on the y-axis.

From this point go UP (rise) another 3 units, then 1 unit to the RIGHT (run), and put another point.  This is the second point.  Connect the points and it should look like this:
{{{graph (300,300, -6,6,-6,6, 3x+2) }}}


EXAMPLE 2:  y = -3x + 2

SOLUTION:
Y-intercept = 2, slope = {{{-3/1 = (rise)/(run) }}}

Start by graphing the y-intercept by going up 2 units on the y-axis.

From this point go DOWN (rise)  3 units, then 1 unit to the RIGHT (run), and put another point.  This is the second point.  Connect the points and it should look like this:
{{{graph (300,300, -6,6,-6,6, -3x+2) }}}


EXAMPLE 3:  y = {{{3/5}}}x + 2

SOLUTION:
Y-intercept = 2, slope = {{{3/5 = (rise)/(run) }}}

Start by graphing the y-intercept by going up 2 units on the y-axis.

From this point go UP (rise) another 3 units, then 5 unit to the RIGHT (run), and put another point.  This is the second point.  Connect the points and it should look like this:
{{{graph (300,300, -6,6,-6,6, (3/5)*x+2) }}}


EXAMPLE 4:  y = {{{-3/5}}}x + 5

SOLUTION:
Y-intercept = 5, slope = {{{-3/5 = (rise)/(run) }}}

Start by graphing the y-intercept by going up 5 units on the y-axis.

From this point go DOWN (rise) 3 units, then 5 unit to the RIGHT (run), and put another point.  This is the second point.  Connect the points and it should look like this:
{{{graph (300,300, -10,10,-10,10, (-3/5)*x+5) }}}


EXAMPLE 5:  y = {{{3/2}}}x -6

SOLUTION:
Y-intercept = -6, slope = {{{3/2 = (rise)/(run) }}}

Start by graphing the y-intercept by going down 6 units on the y-axis.

From this point go UP (rise) another 3 units, then 2 unit to the RIGHT (run), and put another point.  This is the second point.  Connect the points and it should look like this:
{{{graph (300,300, -6,6,-6,6, (3/2)*x-6) }}}