Convert Slope-Intercept to Standard Form worksheet - Free Printable

To convert an equation from slope-intercept form ($y = mx + b$) to standard form ($Ax + By = C$), we follow these general steps:
1. Move the $x$ term to the left side of the equation so that $x$ and $y$ are together.
2. If there are fractions, multiply the entire equation by the least common denominator (LCD) to make all numbers whole integers.
3. Ensure the coefficient of $x$ (the number in front of $x$) is positive.

Here is the step-by-step solution for each problem:

1. $y = \frac{1}{10}x - \frac{3}{5}$
* Subtract $\frac{1}{10}x$ from both sides: $-\frac{1}{10}x + y = -\frac{3}{5}$
* The denominators are 10 and 5. The LCD is 10. Multiply every term by 10:
$10(-\frac{1}{10}x) + 10(y) = 10(-\frac{3}{5})$
$-1x + 10y = -6$
* Make the $x$ coefficient positive by multiplying by $-1$:
$x - 10y = 6$

2. $y = -\frac{5}{7}x - 1$
* Add $\frac{5}{7}x$ to both sides: $\frac{5}{7}x + y = -1$
* Multiply by the denominator 7:
$7(\frac{5}{7}x) + 7(y) = 7(-1)$
$5x + 7y = -7$

3. $y = -7x - 6$
* Add $7x$ to both sides:
$7x + y = -6$
* No fractions to clear, and $x$ is already positive.

4. $y = \frac{3}{7}x + \frac{3}{7}$
* Subtract $\frac{3}{7}x$ from both sides: $-\frac{3}{7}x + y = \frac{3}{7}$
* Multiply by the denominator 7:
$7(-\frac{3}{7}x) + 7(y) = 7(\frac{3}{7})$
$-3x + 7y = 3$
* Make the $x$ coefficient positive by multiplying by $-1$:
$3x - 7y = -3$

5. $y = -\frac{8}{9}x + \frac{1}{3}$
* Add $\frac{8}{9}x$ to both sides: $\frac{8}{9}x + y = \frac{1}{3}$
* The denominators are 9 and 3. The LCD is 9. Multiply every term by 9:
$9(\frac{8}{9}x) + 9(y) = 9(\frac{1}{3})$
$8x + 9y = 3$

6. $y = -\frac{6}{5}x - \frac{7}{5}$
* Add $\frac{6}{5}x$ to both sides: $\frac{6}{5}x + y = -\frac{7}{5}$
* Multiply by the denominator 5:
$5(\frac{6}{5}x) + 5(y) = 5(-\frac{7}{5})$
$6x + 5y = -7$

7. $y = \frac{2}{11}x - \frac{3}{11}$
* Subtract $\frac{2}{11}x$ from both sides: $-\frac{2}{11}x + y = -\frac{3}{11}$
* Multiply by the denominator 11:
$11(-\frac{2}{11}x) + 11(y) = 11(-\frac{3}{11})$
$-2x + 11y = -3$
* Make the $x$ coefficient positive by multiplying by $-1$:
$2x - 11y = 3$

8. $y = -x + \frac{7}{11}$
* Add $x$ to both sides: $x + y = \frac{7}{11}$
* Multiply by the denominator 11:
$11(x) + 11(y) = 11(\frac{7}{11})$
$11x + 11y = 7$

9. $y = \frac{4}{3}x - \frac{5}{3}$
* Subtract $\frac{4}{3}x$ from both sides: $-\frac{4}{3}x + y = -\frac{5}{3}$
* Multiply by the denominator 3:
$3(-\frac{4}{3}x) + 3(y) = 3(-\frac{5}{3})$
$-4x + 3y = -5$
* Make the $x$ coefficient positive by multiplying by $-1$:
$4x - 3y = 5$

10. $y = -\frac{7}{5}x - \frac{8}{5}$
* Add $\frac{7}{5}x$ to both sides: $\frac{7}{5}x + y = -\frac{8}{5}$
* Multiply by the denominator 5:
$5(\frac{7}{5}x) + 5(y) = 5(-\frac{8}{5})$
$7x + 5y = -8$

Final Answer:
1. $x - 10y = 6$
2. $5x + 7y = -7$
3. $7x + y = -6$
4. $3x - 7y = -3$
5. $8x + 9y = 3$
6. $6x + 5y = -7$
7. $2x - 11y = 3$
8. $11x + 11y = 7$
9. $4x - 3y = 5$
10. $7x + 5y = -8$