Pre-Algebra Examples

Graph 6x+3y=11
Step 1
Solve for .
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Step 1.1
Subtract from both sides of the equation.
Step 1.2
Divide each term in by and simplify.
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Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
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Step 1.2.2.1
Cancel the common factor of .
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Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
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Step 1.2.3.1
Cancel the common factor of and .
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Step 1.2.3.1.1
Factor out of .
Step 1.2.3.1.2
Cancel the common factors.
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Step 1.2.3.1.2.1
Factor out of .
Step 1.2.3.1.2.2
Cancel the common factor.
Step 1.2.3.1.2.3
Rewrite the expression.
Step 1.2.3.1.2.4
Divide by .
Step 2
Rewrite in slope-intercept form.
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Step 2.1
The slope-intercept form is , where is the slope and is the y-intercept.
Step 2.2
Reorder and .
Step 3
Use the slope-intercept form to find the slope and y-intercept.
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Step 3.1
Find the values of and using the form .
Step 3.2
The slope of the line is the value of , and the y-intercept is the value of .
Slope:
y-intercept:
Slope:
y-intercept:
Step 4
Any line can be graphed using two points. Select two values, and plug them into the equation to find the corresponding values.
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Step 4.1
Reorder and .
Step 4.2
Find the x-intercept.
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Step 4.2.1
To find the x-intercept(s), substitute in for and solve for .
Step 4.2.2
Solve the equation.
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Step 4.2.2.1
Rewrite the equation as .
Step 4.2.2.2
Subtract from both sides of the equation.
Step 4.2.2.3
Divide each term in by and simplify.
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Step 4.2.2.3.1
Divide each term in by .
Step 4.2.2.3.2
Simplify the left side.
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Step 4.2.2.3.2.1
Cancel the common factor of .
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Step 4.2.2.3.2.1.1
Cancel the common factor.
Step 4.2.2.3.2.1.2
Divide by .
Step 4.2.2.3.3
Simplify the right side.
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Step 4.2.2.3.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 4.2.2.3.3.2
Move the negative in front of the fraction.
Step 4.2.2.3.3.3
Multiply .
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Step 4.2.2.3.3.3.1
Multiply by .
Step 4.2.2.3.3.3.2
Multiply by .
Step 4.2.2.3.3.3.3
Multiply by .
Step 4.2.2.3.3.3.4
Multiply by .
Step 4.2.3
x-intercept(s) in point form.
x-intercept(s):
x-intercept(s):
Step 4.3
Find the y-intercept.
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Step 4.3.1
To find the y-intercept(s), substitute in for and solve for .
Step 4.3.2
Solve the equation.
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Step 4.3.2.1
Remove parentheses.
Step 4.3.2.2
Simplify .
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Step 4.3.2.2.1
Multiply by .
Step 4.3.2.2.2
Add and .
Step 4.3.3
y-intercept(s) in point form.
y-intercept(s):
y-intercept(s):
Step 4.4
Create a table of the and values.
Step 5
Graph the line using the slope and the y-intercept, or the points.
Slope:
y-intercept:
Step 6