Y Intercept Formula

An equation of a straight line is always a linear equation. A linear equation is represented as ax + by = c, where a, and b are the coefficients or the placeholders of constants for the variables, x, and y, respectively.

A is a positive integer, while b and c are integers, where ‘c’ represents an intercept.

So, from the linear equation, we have the following intercept formula:

y  =  c/b

This is the required y intercept formula. A y-intercept ‘c’ of a line is the value of ‘y’ at which the line crosses the y-axis.

There is another equation in the form of y = mx + n, where ‘m’ is the slope of the line and ‘b’ is the y-intercept. This equation is called the slope intercept formula.

On this page, we will understand the y intercept formula with the help of an equation of line graph. 

Along with the intercept formula, we have a look at the slope intercept equation to further understand the slope intercept form calculator with two points.

Equation of Line Graph

The linear equation can be written in the following two forms:

• Ax  +  By  +  C  =  0, and

• Ax  +  By  =  C

So, either way of writing works. Now, let’s say,  you have an equation as x - y   = - 3. Here, we will compare this question with the general equation and plot the graph by putting various values for x and y, as well.

From the General Equation, We Get the Following Details: 

A  =  1

B  =  - 1

C  =  - 3

From (x, y), putting x = 1:

1  -  y   =   -  3 

=>  y  =  4

So, the first coordinate is (1, 4)

Similarly, putting  x =  - 2:

 -  2  -  y   =  - 3   

 =>   y   =  1

The second coordinate is ( - 2, 1)

For the third coordinate, i.e., (3, 6)

Again, putting x = 4, we get our fourth coordinate, i.e., (4, 7)

Now, plotting a graph for the same:

[Image will be Uploaded Soon]

Thus, our condition was that the graph should be straight and yes we got our condition verified.

This means the equation ‘x - y = - 3’ is a linear equation.

Intercept Formula

From the graph, we will have a look at the y-axis, the line which we have drawn as per our obtained coordinates, it cuts at some point on the y-axis, and its value lies between 2 and 4, i.e., 3. So, let’s find it out.

Using the y intercept formula:

y   =   C/B   

Here, C  =   - 3 and B =  -1

y  =  - 3/ -1  =  3

Point To Note:

Please note that the y-intercept is calculated at x = 0. Following the y-intercept, we have an x-intercept formula as well.

For y = 0, the x intercept formula is:

 x   =  C/A  =  - 3/1   =  - 3

Therefore, a straight line cuts the x-axis at - 3. We can see in graph 1 that the line cuts the x-axis between - 2 and  - 4, i.e., - 3; this means our calculation is verified.

Now, besides the intercept formula, we have something slope that a line makes with an axis.

Slope Intercept Formula

A general slope intercept formula of a line is ‘y  =  mx + b.’ Here, c is the intercept (along the y-axis), and ‘m’ is the slope. So, what is the slope?

Let’s suppose that there is a line that cuts at certain points, i..e, (2, 3) and (8, 6), then we get the following graph:

[Image will be Uploaded Soon]

Now, the distance covered by the line at the x-axis and the y-axis is”

 x2 -  x1  =  (8 - 2  =  6), and 

 y2   - y1  =  (6 - 3 =  3), then the slope of a graph formula is:

m  =  \[\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}}\]

Putting the values obtained above, we get:

m =  3/6    =   0.5

So, our slope is 0.5. This means that the slope of a straight line tells us how steep the line is. Also, it is measured in the tangent of an angle.

We know that  m =  tanθ, so, 0.5 = tanθ or m = tan-1 (0.5).

Slope Intercept Formula of a Line

From the slope intercept equation y = mx + b, m is a mnemonic that means ‘move,’ and ‘b’ means where the line begins.

For instance, y = 5x + 6 is a straight line.

So, in-slope intercept form, the equation line represents that m =  5 and b = 6.   

For a slope intercept form calculator with two points, let's find the equation of a line with two points P = (- 1, 5) and Q = (3, 7).  

Here, x1 =  - 1

          y1 =    5

          x2 =  3

          y2 = 7

We know that m = \[\frac{Y_{2}-Y_{1}}{X_{2}-X_{1}}\]

                               = \[\frac{7-5}{3-(-1)}\]  =  1/2     

The intercept for the both the coordinates is:

b   =  y1 -  mx1, and …..(1)

b    =  y2   - mx2 ….(2)

From equation (1):

b =  5  -  (1/2)* -1  =  5 + ½  =  11/2

From equation (2):

b   =  7  - (½)* 3  =  7  - 3/2   =  11/2

We see that the y-intercept for both equations remains the same because it is a single straight line.

So, the slope of a line is ½ or 0.5 or tan-1 (0.5).

The y-intercept between two points is (0, 11/2) or (0, 5.5).

Therefore, the equation of the line in the slope-intercept form is:

 y  =  x/2  + (11/2) y  =  0.5 x  +  5.5 y

Conclusion

In analytical geometry (an insightful calculation), utilizing the normal convention that the horizontal axis addresses a variable x and the vertical axis addresses a variable y and a y-intercept is a point where the graph of a function or connection crosses with the y-axis of the coordinate system. 

The slope of the line is the angle made by a straight line along the axis.