Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 21, 2024

Write inequality $10x + 10y < -10$ in slope-intercept form.

STEP 1

Assumptions
1. We are given an inequality in standard form: $10x + 10y < -10$ .
2. We need to convert this inequality into slope-intercept form, which is $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.
3. Inequalities behave similarly to equations when solving for $y$ , except when multiplying or dividing by a negative number, which reverses the inequality sign.

STEP 2

First, we want to isolate $y$ on one side of the inequality. To do this, we will subtract $10x$ from both sides of the inequality.
$10y < -10x - 10$

STEP 3

Now, we will divide every term by $10$ to solve for $y$ . This will give us the slope-intercept form of the inequality.
$y < -x - 1$

STEP 4

The inequality is now in slope-intercept form. The slope $m$ is $-1$ and the y-intercept $b$ is $-1$ .
The final inequality in slope-intercept form is:
$y < -x - 1$

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