Slope Intercept Form Formula

Slope Intercept Form Formula

The shape of the sloped portion of a straight line is one of the most commonly used shapes to represent the equation of a straight line. Given the slope of the line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis), students can use the Slope Intercept Form Formula to find the equation of the line. The equation of a line is the equation satisfied by any point lying on that line. There are several ways to find this equation for a straight line given as

•  gradient cut shape
• point slope shape
• two point shape
• intercept form

Students must visit Extramarks website to learn more about the Slope Intercept Form Formula.

What Is Slope Intercept Form Of A Straight Line?

A slope profile is a method of finding the equation of a straight line in a coordinate plane. The equation for a straight line is the relationship:

The coordinates of each point on the line are sufficient. Coordinates of non-line points are not filled.Determining this equation is straightforward. To find the Slope Intercept Form Formula of a line,  students  need the slope or slope of that line from the x-axis and the point of intersection with the y-axis. Extramarks provides the best solutions for the Slope Intercept Form Formula.

Slope Intercept Form Definition

The Slope Intercept Form Formula of the straight line is used to find the equation of the straight line. The Slope Intercept Form Formula requires knowing the slope of the line and the point of intersection of the line with the y-axis. Consider a line with slope “m” and y-intercept “b”. The slope-intercept shape formula for a straight line with slopes ‘m’ and ‘b’ as y-intercept is given as y = mx + b.

Slope Intercept Form Examples

Here is an example of the Slope Intercept Form Formula.

The equation for a straight line with slope (-1) and y-intercept (4) is given by y = -x + 4. The slope (2) and origin (y-intercept = 0) are given as y = 2x. Note: The slope of a straight line given a slope angle θ can be calculated as tan θ. Also, given two points (x1, y1) and (x2, y2) on a straight line, the slope is given as (y2 – y1)/(x2 – x1). To better understand the concept, let’s look at the formula for slope intercept and its derivation.

Slope Intercept Formula

The Slope Intercept Form Formula is used to find the slope, y-intercept, x-intercept, or linear formula with the required parameters. Various formulas are available for finding the equation of a straight line. The Slope Intercept Form Formula is one of the formulas used when  students  know the slope of the line (denoted by m) and the y-intercept of the line (denoted by b or (0,b)). Let’s learn theSlope Intercept Form Formula  with some solved examples.

Slope Intercept Formula In Math

formula for slope intercept in mathematics

Using theSlope Intercept Form Formula , the equation for the straight line is

y = mx + b

Where,

m = slope of line

b = y-intercept of the straight line

(x,y) represents each point on the line

When applying the above formula, students need to keep x and y as variables. Note: The Slope Intercept Form Formula cannot be used to find the vertical line formula. Here is an example to understand the use of the Slope Intercept Form Formula.

Example: The equation for a straight line is 3x + 4y + 5 = 0. Use the Slope Intercept Form Formula to determine the slope and y-intercept of the line.

Solution: Rearrange the line equation and write it in the standard form y = mx + b. students have:

4y = -3x – 5 ;y = (-3/4)x + (-5/4)

So m = -3/4, b = -5/4

Answer: Given a straight line with slope m = -3/4 and y-intercept b = -5/4.

Derivation Of Formula For Slope Intercept Form

Consider a line with slope “m” that intersects the y-axis at (0,b) and Its y-intercept is b. Also consider any point (x, y) on the line.

Derivation of the Slope Intercept Form Formula

Let (x1, y1) = (0, b) and (x2, y2) = (x, y).

The slope of the line connecting the two points (x1, y1) and (x2, y2) is m = (y2 – y1)/(x2 – x1).

Using this formula results in the slope of the line above

m = (y – b)/(x – 0)

⇒ m = (y – b)/(x)

Multiply both sides by x,

mx = y – b

add ‘b’ on both sides,

y = mx + b

This is the general Slope Intercept Form Formula for a straight line, including slope and y-intercept. This form of the straight line equation is therefore called the slope-section form, and hence the Slope Intercept Form Formula is derived.

Straight-Line Equation Using Slope Intercept Form

To find the equation for a slanted line, find the slope of the line (or its slope, or its angle θ with the x-axis, etc.) and the line’s placement (i.e., where the line is in relation to the axis; on the y-axis through which the line passes).Students can indicate the location of the line b) by specifying a point, i.e., the y-intercept.These two parameters can be used to uniquely determine each row.

Here are the steps to find the equation of a straight line using the slope intercept:

Step 1: Record the y-intercept “b” and the slope “m” of the line. If the straight line is not given directly and other relevant data is provided, the slope formula can be applied to find the slope of the straight line. Step 2: Then apply theSlope Intercept Form Formula formula, which is: y = mx + b.

Example: A line is slanted at an angle of 60° to the horizontal and passes through the point (0, – 1) and then what will be the equation of the straight line.

Solution: m = tan 60º = √3

So the equation for the straight line is y = mx + c.

⇒y = (√3)x + (−1)

⇒y = √3x − 1

Converting Standard Form To Slope Intercept Form

A straight line equation given in standard form can be converted to slope-intercept form by permuting and comparing. We know that the standard form of the linear equation can be written as Ax + By + C = 0. If  students  sort the terms and find the ‘y’ value they get,

B × y = -Ax – C

⇒y = (-A/B)x + (-C/B),

And (-A/B) will be the slope of the line, and (-C/B) is the y-intercept.

Important note about the Slope Intercept Form Formula:

A line can have a negative slope if the angle with the positive x-direction is obtuse. In this case, the value of tan θ is negative, so m is negative.

For any line through the origin, the y-intercept is (b = 0), so the equation is of the form y = mx.

Examples On Slope Intercept Form

Example 1: Find the equation for the line with slope 1/3 and its y-intercept (0, -5) using the Slope Intercept Form Formula .

Ans: To find the equation of a given straight line:

The y-intercept of the line will be (0, b) = (0, -5) ⇒ b = -5.

Using the Slope Intercept Form Formula, the equation for a given straight line is

y = mx + b

y = (1/3)x – 5

Answer: The equation of the line y = (1/3) x – 5.

Example 2: Find the equation for the horizontal line that intersects the y-axis at (0, 3) then solve for the Slope Intercept Form Formula.

Ans: To find the Slope Intercept Form Formula equation of a given straight line, use the following formula:

Suppose the y-intercept of the line is (0, b) = (0, 3) ⇒ b = 3.

The line is horizontal, so the slope is m = 0.

Using the Slope Intercept Form Formula, the equation for a given straight line is

y = mx + b

y = 0x + 3

y = 3

Answer: The formula for the line given is y = 3.

Example 3: Find the Slope Intercept Form Formula equation of the line parallel to the line y = 3x – 5 with y-intercept (-1/5).

Ans: Find: Equation of a line parallel to the specified line.

Suppose the y-intercept of line B is -1/5.

The equation for a given straight line is

y = 3x – 5

Comparing this to y = mx + b gives a slope of m = 3.

Since the given line is parallel to the requested line, their slopes are equal.

The slope of the line the students are looking for is also M = 3. So, using the Slope Intercept Form Formula, the formula for the line students want is:

y = Mx + B

y = 3x – 1/5

Answer: The Slope Intercept Form Formula equation for the straight line is y = 3x – 1/5.

Practice Questions On Slope Intercept Form

Question 1: Can students  find the Slope Intercept Form Formula equation of the line using slope 6 and y-intercept 4?

Ans:

here,

m = 6 and

b = 4

Formula: y = mx + b

The straight line Slope Intercept Form Formula is y = 6x + 4

Question 2: Express the equation of the line with slope -2 passing through the point (0, 9) in terms of the intercept of the slope.

Ans:

Given the,

slope = m = -2

point = (x, y) = (0, 9)

The equation for a straight line in slope-intercept form is:

y = mx + b….(i)

After being given

9 = (-2)(0) + b

b = 9

Substituting the values of m and b into equation (i), students get

y = -2x + 9

This is the required equation for the slope and intercept of the form lines.

Question 3: Determine the slope and y-intercept of the straight line 2x – y + 5 = 0.

Ans:

Given the linear equation:

2x – y + 5 = 0

therefore,

y = 2x + 5

This is in the form y = mx + b.

So slope = 2 and y-intercept = 5