Lesson Graphing by Slope-Intercept Method

Source code of 'Graphing by Slope-Intercept Method'

This Lesson (Graphing by Slope-Intercept Method) was created by by rapaljer(4671)

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About rapaljer: Retired Professor of Mathematics from Seminole State College of Florida after 36 years.

GRAPHING by SLOPE-INTERCEPT METHOD

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) }}}
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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) }}}
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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) }}}
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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) }}}
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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) }}}
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WHAT IF THE EQUATION OF THE LINE IS NOT IN SLOPE-INTERCEPT FORM?  What if the equation of the line is in STANDARD FORM??

The following problems are ALL given in standard form.  In order to solve by slope and y-intercept method, you will have to solve for y in terms of x for each of them.  Then after you do that, you might want to see my brand new Lesson Plan in algebra.com called Graphing by Slope Intercept Method.

Remember, the first step in each of these is to SOLVE FOR Y in terms of x.
EXAMPLE 6:  x-y = 1

SOLUTION:
x-y = 1
-y = -x + 1
y=x-1

Y intercept is -1, and slope is 1, which is {{{(rise)/(run)= 1/1}}}
{{{graph(300,300,-10,10,-10,10, x-1) }}}
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EXAMPLE 7: x+y=3

SOLUTION:

x+y=3
y = -x + 3
Y-intercept is 3, and slope is -1, which is {{{ (rise)/(run) = -1/1}}}
{{{graph(300,300,-10,10,-10,10, -x+3) }}}
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EXAMPLE 8:  2x-5y=15

SOLUTION:
2x-5y = 15
-5y = -2x + 15

Divide by -5:
{{{(-5y)/-5 = (-2x)/-5 + 15/-5}}}
{{{ y = (2/5)*x - 3 }}}
Y-intercept is -3, and slope is {{{2/5}}}, which is {{{ (rise)/(run) = 2/5}}}
{{{graph(300,300,-10,10,-10,10, (2/5)*x - 3) }}}

R^2 Retired