Write the following inequality in slope-intercept form. 6x + 16y < -3. Write your answer with y first, followed by an inequality symbol. Use integers, proper fractions, and imprope... Write the following inequality in slope-intercept form. 6x + 16y < -3. Write your answer with y first, followed by an inequality symbol. Use integers, proper fractions, and improper fractions in simplest form.
Understand the Problem
The question is asking to rewrite the given inequality, 6x + 16y < -3, in slope-intercept form, which is generally written as y = mx + b, where m is the slope and b is the y-intercept. This involves isolating y on one side of the inequality.
Answer
The slope-intercept form of the inequality is $$ y < -\frac{3}{8}x - \frac{3}{16} $$
Answer for screen readers
The inequality in slope-intercept form is
$$ y < -\frac{3}{8}x - \frac{3}{16} $$
Steps to Solve
- Isolate the term with y To isolate the term with $y$, subtract $6x$ from both sides of the inequality.
[ 16y < -6x - 3 ]
- Divide by the coefficient of y Next, divide both sides of the inequality by 16 to solve for $y$.
[ y < -\frac{6}{16}x - \frac{3}{16} ]
- Simplify the fractions Now, simplify the fractions on the right side.
[ y < -\frac{3}{8}x - \frac{3}{16} ]
The inequality in slope-intercept form is
$$ y < -\frac{3}{8}x - \frac{3}{16} $$
More Information
This inequality expresses the relationship between $x$ and $y$ in a form that makes it easy to identify the slope (-3/8) and the y-intercept (-3/16). The slope indicates a negative relationship, meaning as $x$ increases, $y$ decreases.
Tips
- Forgetting the inequality direction: When you multiply or divide by a negative number, the inequality sign should flip.
- Not simplifying fractions: Always reduce fractions to their simplest form when possible.
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