Inequality to Slope-Intercept Form Calculator

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.

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:

1. Isolate the variable y on one side of the inequality, if it’s not already.
2. Rewrite the inequality with y on the left side and all other terms on the right side.
3. 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:

1. Isolate the variable y: -2y < -3x + 5
2. 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:

1. Isolate the variable y: 2y > -6x + 46
2. 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:

1. Isolate the variable y on one side, if not already done.
2. Rewrite the inequality with y on one side and all other terms on the other side.
3. Solve for y, if possible.
4. 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):

1. Isolate the variable y: -5y = -6x – 15
2. 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:

1. Isolate the variable y: -2y < -3x – 6
2. 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:

1. Isolate the variable y: -5y > -2x + 9
2. 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:

1. Isolate the variable (get it on one side of the inequality).
2. Perform any necessary operations to solve for the variable.
3. 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:

1. Graphical Method: Graph the inequality on a coordinate plane and shade the region that represents the solution set.
2. Algebraic Method: Manipulate the inequality algebraically to isolate the variable and find the solution.
3. 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:

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

1. Convert the inequality to slope-intercept form (if possible).
2. Plot the line corresponding to the equation from step 1.
3. 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.
4. 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−�1m=x2​−x1​y2​−y1​​

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