Slope Intercept Form
The slope intercept form of a straight line is one of the most common forms used to represent the equation of a line. The slope intercept formula can be used to find the equation of a line when given the slope of the straight line and the yintercept(the ycoordinate of the point where the line intersects the yaxis). Equation of line is the equation that is satisfied by each point that lies on that line. There are various methods to find this equation of a straight line given as,
 Slopeintercept form
 Point slope form
 Twopoint form
 Intercept form
Let us understand slope intercept formula, its derivation using solved examples.
What is Slope Intercept Form of a Straight Line?
The slope intercept form is a method used to determine the equation of a straight line in the coordinate plane. The equation of a straight line will be that relation which:
 the coordinates of any point on the line must satisfy.
 the coordinates of any point not on the line will not satisfy.
The determination of this equation is straightforward. To find the slope intercept form of a straight line, we would need the slope, or the angle of inclination of this straight line from the xaxis and the intercept that it makes with the yaxis.
Slope Intercept Form: Definition
The slopeintercept form of a straight line is used to find the equation of a line. For the slopeintercept formula, we have to know the slope of the line and the intercept cut by the line with the yaxis. Let us consider a straight line of slope 'm' and yintercept 'b'. The slope intercept form equation for a straight line with a slope, 'm', and 'b' as the yintercept can be given as: y = mx + b.
Slope Intercept Form: Examples
Some examples of the slope intercept form formula are shown here.
 The equation of a line with slope (1) and yintercept (4) is found using: y = x + 4.
 The equation of a line with slope (2) and passing through origin(yintercept = 0) is given as: y = 2x.
Note: The slope of the line for which angle of inclination, θ is given can be calculated as tan θ. Also, in case when we are given two points (x\(_1\), y\(_1\)) and (x\(_2\), y\(_2\)) lying on the straight line, the slope can be given as: (y\(_2\)  y\(_1\))/(x\(_2\)  x\(_1\)). Let us have a look at the slopeintercept formula and its derivation for a better understanding of the concept.
Slope Intercept Formula
The slopeintercept formula is used to find the slope or the yintercept as well as the xintercept of a straight line. There are different formulas available to find the equation of a straight line. The slopeintercept formula is one of these formulas which is used when we know the slope of the straight line, which is denoted by m, and the yintercept of the straight line, which is denoted by b or (0, b). Let us learn the slopeintercept formula with a few solved examples. Here is the slopeintercept formula.
Slope Intercept Formula in Math:
Using the slopeintercept formula, the equation of the line is:
y = mx + b
where,
 m = the slope of the line
 b = yintercept of the line
 (x, y) represent every point on the line. x and y have to be kept as the variables while applying the above formula.
Note: The slopeintercept formula cannot be applied to find the equation of a vertical line. Here's an example to understand the application of slope intercept formula.
Example : The equation of a line is 3x + 4y + 5 = 0. Determine the slope and yintercept of the line using the slope intercept form.
Solution: We rearrange the equation of the line to write it in the standard form y = mx + b.
We have:
4y = 3x  5
⇒y = (3/4)x + (5/4)
Thus, m = 3/4 , b = 5/4
Answer: The slope of the given straight line, m = 3/4 and the yintercept, b = 5/4.
Derivation of Formula For Slope Intercept Form
Let us consider a line whose slope is 'm' that intersects the yaxis at (0, b), i.e., its yintercept is b. Also, let us consider an arbitrary point (x, y) on the line.
Let us assume that (x\(_1\),y\(_1\)) = (0, b) and (x\(_2\), y\(_2\)) = (x, y).
Using the slope formula, the slope of a line joining two points (x\(_1\), y\(_1\)) and (x\(_2\), y\(_2\)) is, m = (y\(_{2}\)  y\(_{1}\))/(x\(_{2}\)  x\(_{1}\))
Using this formula, the slope of the above line is,
m = (y  b) / (x  0)
⇒ m = (y  b) / (x)
Multiplying both sides by x,
mx = y  b
Adding 'b' on both sides,
y = mx + b
This is the general equation of a straight line involving its slope and its yintercept. This form of the equation of the line is therefore termed the slopeintercept form. Hence the slope intercept formula is derived.
StraightLine Equation Using Slope Intercept Form
To find the equation of a line with an arbitrary inclination, we would need two quantities: the inclination of the line (or its slope or the angle, θ, it makes with say, the xaxis) and the placement of the line (i.e. where the line passes through with reference to the axes; we can specify the placement of the line by specifying the point on the yaxis through which the line passes, or in other words, by specifying the yintercept, b). Any line can be determined uniquely using these two parameters.
The steps to find the equation of a line using the slopeintercept form are given below,
Step 1: Note down the yintercept, 'b', and the slope of the line as 'm'. We can apply the slope formula to find the slope of any straight line, in case it is not given directly and other relevant data is provided.
Step 2: Apply the slope intercept formula: y = mx + b.
Example: A line is inclined at an angle of 60° to the horizontal, and passes through the point (0,  1). Find the equation of the line.
Solution: We have, m = tan 60º = √3
Thus, the equation of the line is, y = mx + c
⇒y = (√3)x + (−1)
⇒y = √3x − 1
Converting Standard Form to Slope Intercept Form
We can convert the equation of a line given in the standard form to slope intercept form by rearranging and comparing. We know that the standard form of the equation of a straight line can be given as, Ax + By + C = 0. Rearranging the terms to find the value of 'y', we get,
B × y = Ax  C
⇒y = (A/B)x + (C/B),
where (A/B) makes the slope of the line and (C/B) is the yintercept.
Topics Related to Slope Intercept Form:
Important Notes on Slope Intercept Form:
 A line may have a negative slope – in case the angle it makes with the positive xdirection is an obtuse angle. The value of tan θ, in this case, will be negative, so m will be negative.
 For any line passing through the origin, the yintercept will be (b = 0), so its equation will be of the form: y = mx.
Examples on Slope Intercept Form

Example 1: Using the slope intercept form, find the equation of a straight line with slope 1/3 and whose yintercept is (0, 5).
Solution:
To find the equation of the given line:
Given: the slope of the line is m = 1/3.
the yintercept of the line is (0, b) = (0, 5) ⇒ b = 5.
Using the slopeintercept formula, the equation of the given line is,
y = mx + b
y = (1/3) x  5
Answer: The equation of the given line is, y = (1/3) x  5.

Example 2: Find the equation of the horizontal line that intersects the yaxis at (0, 3). Solve it using the slopeintercept formula.
Solution:
To find the equation of the given line:
It is given that the yintercept of the line is (0, b) = (0, 3) ⇒ b = 3.
Since the line is horizontal, its slope is m = 0.
Using the slopeintercept formula, the equation of the given line is,
y = mx + b
y = 0x + 3
y = 3
Answer: The equation of the given line is, y = 3.

Example 3: Find the equation of a line that is parallel to the line y = 3x  5 and whose yintercept is 1/5.
Solution:
To find: The equation of the line parallel to the given line.
It is given that the yintercept of the line is B = 1/5.
The equation of the given line is,
y = 3x  5
Comparing this with y = mx + b, we get its slope to be m = 3.
Since the given line is parallel to the required line, their slopes are equal.
So the slope of the required line is, M = 3 as well.
Thus the equation of the required line using the slopeintercept formula is,
y = Mx + B
y = 3x  1/5
Answer: The equation of the required line is, y = 3x  1/5.
FAQs on Slope Intercept Form
What is Slope Intercept Form in Math?
The slope intercept form in math is one of the forms used to calculate the equation of a straight line, given the slope of the line and intercept it forms with the yaxis. The slope intercept form is given as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the yintercept.
What is the Slope Intercept Form Equation?
The slope intercept equation is used to find the general equation of a straight line using its slope and the point where it intersects the yaxis. Slope intercept form equation is given as, y = mx + b.
How do you Find SlopeIntercept Form?
The slope intercept form of any line can be calculated simply using the slope and yintercept. The slope intercept form of a straight line is given as,
y = mx + b
where,
 (x, y) is an arbitrary point on the line
 m is the slope of the line
 b is the yintercept
How to Find the Equation of a Straight Line Using Slope Intercept Form?
We need the slope of the straight line and its point of intersection with the yaxis to find the straightline equation using the slope intercept form. The slope of a line can be calculated using the slope formula. Using the slope intercept form, equation of straight line can be calculated as, y = mx + b, where 'm' is the slope of the straight line and 'b' is the yintercept.
What is SlopeIntercept Formula?
The slopeintercept formula is one of the formulas used to find the equation of a line. The slopeintercept formula of a line with slope m and yintercept b is, y = mx + b. Here (x, y) is any point on the line.
How To Derive the SlopeIntercept Formula?
Let us consider a line whose slope is m and whose yintercept is (0, b). To find the equation of the line, consider a random point (x, y) on it. Then using the slope formula, (y  b) / (x  0) = m. Solving it for y, we get y = mx + b.
What are the Applications of the SlopeIntercept Formula?
The slopeintercept formula is used to
 find the equation of a line.
 graph a line using the yintercept and slope.
 find the slope of a line easily.
 find the intercepts of a line easily.
How to Find the Slope of a Line Using the SlopeIntercept Form?
We can find the slope of a line using the slopeintercept form given as, y = mx + b, where 'm' is the slope of the line and 'b' is the yintercept. Here is an example. Let us find the slope of the line 6x  3y = 5. Let us solve this for 'y' to get into the slopeintercept form. Then we get y = 2x  (5/3). Comparing this with the slopeintercept formula, y = mx + b, we get its slope to be m = 2.
How to Convert Standard Form of Straight Line Equation to Slope Intercept Form?
The standard form of equation of a straight line is given as, Ax + By + C = 0. Rearranging this standard form, we can find the slope intercept of any straight line given in this form as, y = (A/B)x + (C/B), where (A/B) makes the slope of the line and (C/B) is the yintercept.
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