Write The Following Inequality in Slope Intercept Form Calculator

This guide explains how to convert linear inequalities to slope-intercept form (y = mx + b) using our calculator. Slope-intercept form is a standard way to represent linear equations and inequalities in mathematics.

What is Slope-Intercept Form?

Slope-intercept form is a way to write linear equations in the form:

y = mx + b

Where:

y is the dependent variable (what we're solving for)
m is the slope (rate of change)
x is the independent variable
b is the y-intercept (where the line crosses the y-axis)

For inequalities, we use the same form but with inequality signs:

y > mx + b
y < mx + b
y ≥ mx + b
y ≤ mx + b

How to Convert an Inequality to Slope-Intercept Form

To convert a linear inequality to slope-intercept form, follow these steps:

Start with the given inequality
Isolate the term with y on one side
Combine like terms on the other side
Divide all terms by the coefficient of x to solve for y
Write the final inequality in slope-intercept form

Note: The inequality sign remains the same when multiplying or dividing by a positive number. If you multiply or divide by a negative number, you must reverse the inequality sign.

Example Conversion

Let's convert the inequality 2x - 3y ≤ 6 to slope-intercept form:

Start with: 2x - 3y ≤ 6
Add 3y to both sides: 2x ≤ 3y + 6
Subtract 6 from both sides: 2x - 6 ≤ 3y
Divide all terms by 3: (2x)/3 - 2 ≤ y
Simplify: (2/3)x - 2 ≤ y

The final slope-intercept form is:

y ≥ (2/3)x - 2

Common Mistakes to Avoid

Forgetting to reverse the inequality sign when multiplying or dividing by a negative number
Incorrectly combining like terms
Dividing by the wrong coefficient (must divide by the x coefficient)
Not simplifying the final expression

FAQ

What is the difference between slope-intercept form and standard form?: Slope-intercept form (y = mx + b) shows the slope and y-intercept directly. Standard form (Ax + By = C) shows the x and y intercepts.
Can all linear inequalities be written in slope-intercept form?: Yes, any linear inequality can be rewritten in slope-intercept form by isolating y.
How do I know if I've done the conversion correctly?: Check that you've isolated y on one side, combined like terms correctly, and maintained the proper inequality sign.
What if the inequality has no solution?: If you end up with a statement like 0 > 5, the inequality has no solution. This means the original inequality is never true.