# Derive the Slope Intercept form and explain it with the help of examples.

Linear equation y = mx + c graphs is a line having m as a slope and c and m as the y-intercept. This type of linear equation is known as a slope-intercept form where m and c are real numbers. Slope m shows the steepness of a line.

Slope basically shows the change in a vertical position as well as in a horizontal position commonly used formula is rise/run and read as “rise over run”. Let slope m = 3/7 which means the object move 3 units up for every 7 units that it goes over.

For a two-point slope intercept use the formula m = (y2 – y1 / x2 – x1). There are two coordinate planes in a rectangular coordinate system x and y if one of them crosses by line then where it crosses is an intercept.

Moreover, in this article, the basic definition formula and concise and useful information regarding to slope intercept will be discussed with the help of examples.

## Slope intercept form

In slope-intercept form, a y-intercept is a point where the line touch with the y-axis. On the other hand, the y-axis is vertically moved up and down. The equation of the line in its working uses a y-intercept where the lines cross the y-axis.

In mathematical it is written as:

y = mx + c

Here,

• m is the slope
• y shows y coordinate
• x shows x coordinate
• c shows y-intercept

## Use of slope intercept formula

The slope-intercept formula is very helpful in these things

• Draw a graph of a line with the slope and y-intercept
• Determining slope in an easy way

## With the help of a standard form, the equation derives the slope-intercept form

It is understood that the standard form of the equation for the straight line is:

L(x) + M(y) + N = 0 where L, M and N are arbitrary constants

Now re-arranging terms

M(y) = -L(x) – N

Divide by M into both sides

y = (-L/M) (x) + (-N/M)

Which is slope intercept form y = m(x) + c

Here, (-L/M) represents the slope of the line and (-N/M) is the y-intercept.

## Example Sections

In this section with the help of examples, the topic will be explained and the equation of straight lines will calculate with the help of the slope-intercept form formula.

Example 1:

Find the equation of the straight- line having slope = 2 and touching the x and y coordinates at point (2,5).

Solution:

With the help of the slope-intercept form a formula equation of a straight line.

y = m(x) +c

Step 1:

Extract the given data

Slope = m = 2

From the statement of a problem, points are

x = 2 & y = 5

Step 2:

Now replacing the values x with 2 and y with 5 to get the equation of a straight line.

y = mx + c

(5) = 2*2 + c

(5) = 4 + c

c = 5-4 = 1

Thus, the Hence, the given equation of the straight line would be;

y = 2x+1

A slope intercept form calculator by Allmath is a handy tool to derive slope intercept form equation with the help of slope and coordinate points.

Example 2:

Determine the slope of a line passing from these points (1, -2) and (3,-6).

Solution:

Step 1:

Extract the given data

Point A = (1, -2)

Point B = (3, -6)

Step 2:

To find the slope of two points here is the formula below just put the values to get the slope

Slope = m = y2 – y1 / x2 – x1

Step 3:

Now replacing the values y2 with -6 and y1 with -2 and x2 with 3 and x1 with 1

m = -6 – (-2) / 3 -1

m = -6 + 2 / 2

m = -4 / 2

m = -2

Example 3:

Find the equation of the straight-line passing through these points (3,7) and (5,8) and c = 3

Solution:

With the help of the slope-intercept form a formula equation of a straight line.

y = m(x) +c

Step 1:

To find the equation of a straight line two-point slope formula will be used.

m = y2 – y1 / x2 – x1

Slope = m = 8 – 7 / 5 – 3 = 1 / 2

Step 2:

Now replacing the values m with 1/2 and c with 3 to get the equation of a straight line.

y = mx + c

y = (½) x + 3

Thus, the Hence, the given equation of the straight line would be;

y = (½) x + 3

Example 4:

Find the equation of the straight- line having slope = 1 and touching the x and y coordinates at point (3,7).

Solution:

With the help of the slope-intercept form a formula equation of a straight line.

y = m(x) +c

Step 1:

Extract the given data

Slope = m = 1

From the statement of a problem, points are

x = 3 & y = 7

Step 2:

Now replacing the values x with 3 and y with 7 to get the equation of a straight line.

y = mx + c

(7) = 1*3 + c

(7) = 3 + c

c = 7-3 = 4

Thus, the Hence, the given equation of the straight line would be;

y = x+4

## Conclusion

In this article, you have studied the basic idea of slope intercept its formula, and its use in our calculations. Moreover, how to derive slope intercept formula using standard form equation and later on with the help of example topic is explained.

We hope anyone can easily defend this topic after a complete understanding of this article.