Write the following inequality in slope-intercept form. 6x - y < 10
Understand the Problem
The question is asking to rewrite the inequality '6x - y < 10' into slope-intercept form (y = mx + b), which involves isolating y on one side of the inequality.
Answer
$$ y > 6x - 10 $$
Answer for screen readers
$$ y > 6x - 10 $$
Steps to Solve
- Starting with the original inequality
We begin with the inequality:
$$ 6x - y < 10 $$
- Isolating the term with y
To isolate $y$, we can rearrange the inequality. First, subtract $6x$ from both sides:
$$ -y < -6x + 10 $$
- Removing the negative sign
Next, we need to multiply the entire inequality by -1. Remember, when you multiply or divide an inequality by a negative number, you must flip the inequality sign:
$$ y > 6x - 10 $$
- Rearranging to slope-intercept form
Now we have the inequality in slope-intercept form.
Thus, the final inequality is:
$$ y > 6x - 10 $$
$$ y > 6x - 10 $$
More Information
The inequality $y > 6x - 10$ represents a region above the line $y = 6x - 10$. This means that for any value of $x$, the corresponding value of $y$ must be greater than what is given by the line.
Tips
- Forgetting to flip the inequality symbol when multiplying or dividing by a negative value.
- Misplacing or incorrectly rearranging terms during the isolation of $y$.
To avoid these, always double-check the operations on both sides of the inequality.
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