Put the following equation of a line into slope-intercept form, simplifying all fractions: 3x + 6y = 36
Understand the Problem
The question is asking us to convert the given equation of a line, 3x + 6y = 36, into slope-intercept form (y = mx + b) while simplifying all fractions.
Answer
The equation in slope-intercept form is $$ y = -\frac{1}{2}x + 6 $$
Answer for screen readers
The slope-intercept form of the equation is $$ y = -\frac{1}{2}x + 6 $$
Steps to Solve
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Isolate the term with y We start with the equation (3x + 6y = 36). To isolate (6y), we subtract (3x) from both sides: $$ 6y = 36 - 3x $$
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Rearrange the equation Next, we want to write the equation in a form that directly shows the slope and the y-intercept. We can rearrange this to: $$ 6y = -3x + 36 $$
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Divide by the coefficient of y To solve for (y), divide every term by (6): $$ y = -\frac{3}{6}x + \frac{36}{6} $$
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Simplify the fractions We simplify the fractions: $$ y = -\frac{1}{2}x + 6 $$
Now, the equation is in slope-intercept form (y = mx + b) where (m) is the slope and (b) is the y-intercept.
The slope-intercept form of the equation is $$ y = -\frac{1}{2}x + 6 $$
More Information
This equation indicates that the slope of the line is (-\frac{1}{2}) and the y-intercept is (6). This means that for every unit increase in (x), (y) decreases by (\frac{1}{2}).
Tips
- Not isolating y properly: Students might forget to correctly move (3x) to the other side when rearranging the equation.
- Forgetting to simplify fractions: It's important to ensure that all fractions are simplified in the final form of the equation.
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