To convert an inequality to slope-intercept form, isolate the variable y, if possible. Rewrite the inequality with y on one side and all other terms on the other side. Then, solve for y to express it explicitly in terms of x. This results in an equation in the form y = mx + b, where ‘m’ represents the slope and ‘b’ represents the y-intercept.

## Inequality to Slope-Intercept Form Calculator

Converting linear inequalities into slope-intercept form (y = mx + b) involves isolating the variable y on one side. Below is a table that summarizes the process for various inequality symbols:

Inequality Symbol | Conversion to Slope-Intercept Form |
---|---|

< | Isolate y and rewrite the inequality as y < mx + b |

> | Isolate y and rewrite the inequality as y > mx + b |

≤ | Isolate y and rewrite the inequality as y ≤ mx + b |

≥ | Isolate y and rewrite the inequality as y ≥ mx + b |

In each case, ‘m’ represents the slope, and ‘b’ represents the y-intercept. Once you’ve converted the inequality, you have it in slope-intercept form, suitable for graphing and analysis.

## FAQs

**How do you convert an inequality to slope-intercept form?** To convert an inequality to slope-intercept form (y = mx + b), you typically follow these steps:

- Isolate the variable y on one side of the inequality, if it’s not already.
- Rewrite the inequality with y on the left side and all other terms on the right side.
- Solve for y to express it explicitly in terms of x.

**What is the intercept form of the inequality?** The intercept form of an inequality is not a standard mathematical notation. However, if you mean the standard form of a linear inequality, it is usually written as Ax + By < C or Ax + By > C, where A, B, and C are constants.

**How do you write an inequality in point-slope form?** Point-slope form of an inequality for a line is not commonly used. Point-slope form is usually used for writing equations of lines, not inequalities. It is written as y – y1 = m(x – x1), where (x1, y1) is a point on the line, and m is the slope.

**What is the equation of the line using slope-intercept form calculator?** You can use a slope-intercept form calculator to find the equation of a line given its slope (m) and y-intercept (b). The equation will be in the form y = mx + b.

**What would be the slope-intercept form for the inequality 3x − 2y < 5?** To convert the inequality 3x – 2y < 5 to slope-intercept form:

- Isolate the variable y: -2y < -3x + 5
- Divide both sides by -2 (remember to reverse the inequality when dividing by a negative number): y > (3/2)x – 5/2

So, the slope-intercept form for the inequality is y > (3/2)x – 5/2.

**What is the slope-intercept form of the inequality 6x + 2y > 46?** To convert the inequality 6x + 2y > 46 to slope-intercept form:

- Isolate the variable y: 2y > -6x + 46
- Divide both sides by 2: y > (-6/2)x + 46/2

Simplify: y > -3x + 23

So, the slope-intercept form for the inequality is y > -3x + 23.

**How do you solve an inequality in standard form?** To solve an inequality in standard form (Ax + By < C or Ax + By > C), you typically follow these steps:

- Isolate the variable y on one side, if not already done.
- Rewrite the inequality with y on one side and all other terms on the other side.
- Solve for y, if possible.
- Determine the appropriate solution set based on the inequality symbol (<, >, ≤, ≥).

**How do you find the y-intercept of an inequality?** To find the y-intercept of an inequality in standard form (Ax + By < C or Ax + By > C), you can set x = 0 and solve for y. The value of y obtained will be the y-intercept of the inequality.

**How do you write an inequality for a line?** To write an inequality for a line, you can use the slope-intercept form (y = mx + b) of the line and include the desired inequality symbol (<, >, ≤, ≥) to represent the region above or below the line. For example, for the line y = 2x + 3, you can write the inequality as y ≥ 2x + 3 to represent the region above the line.

**What is the slope of the line in the linear inequality?** The slope of a line in a linear inequality (Ax + By < C or Ax + By > C) is represented by the coefficient of x in the slope-intercept form of the line (y = mx + b). The slope is denoted by ‘m.’

**What is the slope-intercept form of 6x – 5y = -15?** To write the equation 6x – 5y = -15 in slope-intercept form (y = mx + b):

- Isolate the variable y: -5y = -6x – 15
- Divide both sides by -5 (remember to reverse the inequality when dividing by a negative number): y = (6/5)x + 3

So, the slope-intercept form of the equation is y = (6/5)x + 3.

**What is the slope of 3x – 2y < -6?** To find the slope of the line represented by the inequality 3x – 2y < -6, you can first rewrite it in slope-intercept form:

- Isolate the variable y: -2y < -3x – 6
- Divide both sides by -2 (remember to reverse the inequality when dividing by a negative number): y > (3/2)x + 3

The slope of the line is (3/2).

**What is the slope of the line 2x – 5y > 9?** To find the slope of the line represented by the inequality 2x – 5y > 9, you can first rewrite it in slope-intercept form:

- Isolate the variable y: -5y > -2x + 9
- Divide both sides by -5 (remember to reverse the inequality when dividing by a negative number): y < (2/5)x – 9/5

The slope of the line is (2/5).

**What are the 3 steps to solving an inequality?** The 3 steps to solving a linear inequality are:

- Isolate the variable (get it on one side of the inequality).
- Perform any necessary operations to solve for the variable.
- Determine the solution set based on the inequality symbol (<, >, ≤, or ≥).

**What are the 3 ways to solve an inequality?** Three common methods to solve linear inequalities are:

**Graphical Method:**Graph the inequality on a coordinate plane and shade the region that represents the solution set.**Algebraic Method:**Manipulate the inequality algebraically to isolate the variable and find the solution.**Test Point Method:**Choose a test point (usually (0,0)) and substitute it into the inequality to determine if it satisfies the inequality. If it does, all points on one side of the inequality satisfy it.

**How do you solve an inequality 4x + 7 < 5?** To solve the inequality 4x + 7 < 5:

- Subtract 7 from both sides: 4x < 5 – 7
- Simplify: 4x < -2
- Divide both sides by 4 (remember to reverse the inequality when dividing by a negative number): x > -2/4
- Simplify further: x > -1/2

So, the solution to the inequality is x > -1/2.

**How do you graph inequalities step by step?** To graph an inequality step by step:

- Convert the inequality to slope-intercept form (if possible).
- Plot the line corresponding to the equation from step 1.
- Determine the shading region based on the inequality symbol (<, >, ≤, or ≥). For example, for y > mx + b, shade above the line; for y < mx + b, shade below the line.
- Optionally, label the solution region if needed.

**How do you find the slope of an equation?** To find the slope of an equation in the form y = mx + b, the slope ‘m’ is the coefficient of ‘x’ in the equation.

**What is the formula for the slope function?** The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) on a line is: �=�2−�1�2−�1*m*=*x*2−*x*1*y*2−*y*1

This formula represents the change in y divided by the change in x between the two points on the line.

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