# SLOPE INTERCEPT FORM EQUATION OF A LINE

## About "Slope intercept form equation of a line"

"Slope intercept form equation of a line" is probably the most frequently used way  to express equation of a line.

Here, we will form equation of a straight line using slope and y - intercept.

Slope - Intercept form equation of a line  Here,

Slope of the line  =  m

y-intercept  =  b

## Slope intercept form equation of a line - Practice problems

Problem 1 :

Find the slope and y-intercept of the straight line whose equation is 4x - 2y + 1 = 0.

Solution :

Since we want to find the slope and y-intercept, let us write the given equation 4x - 2y + 1 = 0 in slope-intercept form.

4x - 2y + 1 = 0 ----------> 4x + 1 = 2y

(4x + 1)/2  =  y ---------> 2x + 1/2  =  y

or   y  =  2x + 1/2

The above form is slope intercept form.

If we compare y  =  2x + 1/2  and  y  =  mx + b,

we get   m  =  2     and     b  =  1/2

Hence, the slope is 2 and y-intercept is 1/2

Problem 2 :

A straight line has the slope 5. If the line cuts y-axis at "-2", find the general equation of the straight line.

Solution :

Since the line cuts y-axis at "-2", clearly y-intercept is "-2"

Now, we know that slope m = 5 and y-intercept b = -2.

Equation of straight in slope-intercept form is

y  =  mx + b

Plugging m  =  5  and  b  =  -2,  we get    y  = 5x - 2

y  = 5x - 2 ---------> 5x - y - 2  =  0

Hence, the general equation of the required line is 5x - y - 2 = 0

## Using slope intercept form as linear cost function

One of the major applications of "Slope intercept form equation of a line" is, it can be used as linear cost function in business.

"Linear cost function" is the function where the cost curve of a particular product will be a straight line. It is a confusable topic for some students who study the topic "Different forms equation of straight line" in algebra in both school and college level math.

Mostly this function used to find the total cost of "n" units of the products produced.

For any product, if the cost curve is linear, the linear cost function of the product will be in the form of

y = Ax + B

Here, "y" stands for total cost

"x" stands for number of units.

"A" stands for cost of one unit of the product

"B" stands for fixed cost.

Linear cost function is called as bi parametric function. Here the two parameters are "A" and "B".

Once the two parameters "A" and "B" are known, the complete function can be known.

## How to solve word problems on linear cost function ?

The following steps are involved in solving word problems on linear cost function.

Step 1 :

First we have to go through the question carefully and understand the information given in the question.

After having gone through the question, we have to conclude whether the information given in the question fits linear-cost function.

If the information fits the linear-cost function, we have to follow step 2

Step 2 :

Target : We have to know what has to be found.

In linear-cost function, mostly the target would be to find either the value of "y" (total cost) or "x" (number of units).

Step 3 :

In step 3,  we have to calculate the two constants "A"  and "B" from the information given in the questions. It has been shown clearly in the example problem given below.

Step 4 :

Once the values of "A" and "B"  in   y = Ax + B are found, the linear-cost function would be completely known.

Step 5 :

After step 4, based on the target of the question, we have to find either the value of "y" or "x" for the given input.

For example, if the value of "x" (number of units) is given, we can find the value of "y" (total cost).

If the value of "y" (total cost) is given, we can find the value of "x" (number of units).

## Example Problem

To understand the application of "Slope intercept form equation of a line", let us go through the following problem on linear cost function.

Problem :

A manufacturer produces 80 units of a particular product at a cost of \$ 220000 and 125 units at a cost of \$ 287500. Assuming the cost curve to be linear, find the cost of 95 units.

Solution :

Step 1 :

When we go through the question, it is very clear that the cost curve is linear.

And the function which best fits the given information will be a linear-cost function.

That is,                              y = Ax + B

Here "y" --------> Total cost

"x" --------> Number of units

Step 2 :

Target : We have to find the value of "y" for "x = 95"

Step 3 :

From the question, we have

x = 80        and       y = 220000

x = 75        and       y = 287500

Step 4 :

When we plug the above values of "x" and "y" in y = Ax + B, we get

220000 = 80A + B

287500 = 75A + B

Step 5 :

When we solve the above two linear equations for A and B, we get                      A  =  1500   and    B  =  100000

Step 6 :

From A = 1500 and B = 100000, the linear-cost function for the given information is
y  = 1500x  +  100000

Step 7 :

To estimate the value of "y" for "x = 95", we have to plug "x = 95" in "y = 1500x + 100000"

y = 1500x95 + 100000

y = 142500  +  100000

y = 242500

Hence, the cost of 95 units is \$ 242500

After having gone through above stuff, we hope that students would have understood the stuff "Slope intercept form equation of a line".

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