Lesson Graphing Equations in Standard Form by Two-Intercept Method

Source code of 'Graphing Equations in Standard Form by Two-Intercept Method'

This Lesson (Graphing Equations in Standard Form by Two-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 EQUATIONS in STANDARD FORM by the TWO-INTERCEPT METHOD

When the equation of a line is given in STANDARD FORM, so the easiest way to graph it is probably the TWO-INTERCEPT METHOD.  Instead of having to solve for y in terms of x in order to find the slope and y-intercept, I think it is much easier to just find the x and y intercepts.

EXAMPLE 1: 2x+y = -2

SOLUTION:

2x+y = -2

If x= 0, then y = -2
If y=0, then 2x= -2, so x= -1
Graph these points and connect the dots.  It should look like this:

{{{graph(300,300, -6,6,-6,6, -2x-2) }}}
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EXAMPLE 2:  3x-6y=-3

SOLUTION:

3x - 6y = -3

If x = 0, then -6y=-3, so y= {{{1/2}}}
If y=0, then 3x = -3, so x = -1
Graph these points and connect the dots.  It should look like this:

{{{graph(300,300, -6,6,-6,6, (1/2)*x+(1/2)) }}}

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EXAMPLE 3:  -2x+y=-2

SOLUTION:

-2x + y = -2

If x = 0, then y=-2
If y=0, then -2x = -2, so x = 1
Graph these points and connect the dots.  It should look like this:

{{{graph(300,300, -6,6,-6,6, 2x-2) }}}

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EXAMPLE 4:  {{{(1/4)*x+(3/4)*y=6}}}

SOLUTION:

{{{(1/4)*x+(3/4)*y=6}}}

First multiply both sides by the LCD which is 4:
{{{4*(1/4)x+4*(3/4)y=4*6}}}
{{{x + 3y = 24}}}

If x = 0, then 3y=24, so y= 8
If y=0, then x = 24  (This will take a LARGE GRAPH!)

Graph these points and connect the dots.  It should look like this:

{{{graph(300,300, -10,30,-10,30, (-1/3)*x+8 )}}}

R^2 Retired