Example of Converting from Slope Intercept to Standard Form
Example
Convert $$ y = \frac 5 4 x + 5 $$, graphed on the right, to standard form.
Step 1
Multiply by the least common denominator of the fractions (if any)
The only fraction is $$ \frac { 5}{ \red 4} $$ so you can multiply everything by 4.
$ \red 4 \cdot y = \red 4 \cdot \big( \frac { 5}{ \red 4}x +5 \big) \\ 4y = 5x + 20 $
Step 2
Move" y1 to the other side by adding its opposite to both sides of the equation and simplify
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Practice Problems
Problem 1
Step 1
Multiply by the least common denominator of the fractions
The only fraction is $$ \frac{2}{\red 3 } $$ so you can multiply everything by 3.
$$ \red 3 \cdot y = \red 3 \big( \frac{2}{\red 3 } -4 \big) \\ 3y = 2x-12 $$
Step 2
Step 1
Multiply by the least common denominator of the fractions (if any)
The only fraction is $$ \frac{1}{\red 2}$$ so you can multiply everything by 2.
$$ \red 2 \cdot y =\red 2 \cdot \big( \frac{1}{\red 2} x + 5 \big) \\2y = x + 10 $$
Step 2
Step 1
Multiply all terms by the least common denominator of the fractions
Unlike the prior examples, this problem has two fractions $$ \big( \frac 2 3 \text{ and } \frac 5 9 \big) $$ so you can multiply everything by their common denominator of $$ \red 9$$ .
$$ \red 9 \cdot y = \red 9 \big( \frac 2 3 x + \frac 5 9 \big) \\ 9y = 6x + 5 $$
Step 2
Step 1
Multiply all terms by the least common denominator of the fractions
This problem only has the fraction $$ \frac{4}{\red 7 } $$ so we must multiply everything by 7.
$$ \red 7 \cdot y = \red 7 \big( 5x + \frac 4 7 \big) \\ 7y = 35x + 4 $$
Step 2
Problem 5
Convert the the equation below from slope intercept to standard from (yes, this is a very challenging problem so let's see how sharp your algebra skills are.) $ y = ax + \frac b c $
Step 1
Multiply all terms by the least common denominator of the fractions
This problem only has the fraction $$ \frac{b}{ \red c } $$ so we must multiply everything by $$ \red c $$.
$$ \red c \cdot y = \red c \big( ax + \frac b c \big) \\ cy = cax + b $$ .
Step 2
- Related Links:
- Linear Equations
- Equation of Line Formula
- Slope Intercept Form
- Standard Form of Line
- Standard Form to Slope intercept form
- Linear Equations Worksheets (standard form, slope intercept form and more)