Write the following inequality in slope-intercept form: 16x - y ≥ 3.
Understand the Problem
The question is asking to rearrange the given inequality into slope-intercept form, which is typically expressed as y = mx + b, where m is the slope and b is the y-intercept. The provided inequality is 16x - y ≥ 3.
Answer
$y \leq 16x - 3$
Answer for screen readers
The inequality in slope-intercept form is: $$ y \leq 16x - 3 $$
Steps to Solve
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Rewrite the inequality for y To rearrange the inequality, we need to isolate $y$ on one side. Start by moving $16x$ to the right side: $$ -y \geq 3 - 16x $$
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Multiply by -1 and reverse the inequality Next, multiply both sides of the inequality by -1. Remember to reverse the inequality symbol when multiplying by a negative number: $$ y \leq -3 + 16x $$
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Rearrange in slope-intercept form Now, we rewrite the inequality to clearly show the slope-intercept form $y = mx + b$: $$ y \leq 16x - 3 $$
The inequality in slope-intercept form is: $$ y \leq 16x - 3 $$
More Information
This form indicates that the slope of the line is 16 and the y-intercept is -3. The curve of the graph will be below the line since it is a "less than or equal to" inequality.
Tips
- Not reversing the inequality sign: When multiplying or dividing by a negative number, always remember to reverse the inequality symbol.
- Incorrectly isolating y: Make sure to carefully move terms across the inequality sign.
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