Linear Algebra Examples

Step 1
Solve for .
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Step 1.1
Rewrite the equation as .
Step 1.2
Subtract from both sides of the equation.
Step 1.3
Divide each term in by and simplify.
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Step 1.3.1
Divide each term in by .
Step 1.3.2
Simplify the left side.
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Step 1.3.2.1
Cancel the common factor of .
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Step 1.3.2.1.1
Cancel the common factor.
Step 1.3.2.1.2
Divide by .
Step 1.3.3
Simplify the right side.
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Step 1.3.3.1
Simplify each term.
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Step 1.3.3.1.1
Dividing two negative values results in a positive value.
Step 1.3.3.1.2
Dividing two negative values results in a positive value.
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 2.3
Reorder terms.
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
Write in form.
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Step 4.1.1
Reorder and .
Step 4.1.2
Reorder terms.
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
Combine and .
Step 4.2.2.3
Subtract from both sides of the equation.
Step 4.2.2.4
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
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
Multiply by .
Step 4.3.2.2
Remove parentheses.
Step 4.3.2.3
Simplify .
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Step 4.3.2.3.1
Multiply by .
Step 4.3.2.3.2
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