WORKSHEET ON SLOPE INTERCEPT FORM EQUATION OF A LINE

Problem 1 :

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

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. 

Problem 3 :

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. 

Answers

1. Answer :

Because 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

Divide each side by 2. 

(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

So, the slope is 2 and y-intercept is 1/2. 

2. Answer :

Because 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 a straight line in slope-intercept form is

y  =  mx + b

Substitute 5 for m and -2 for b.

y  =  5x - 2

5x - y - 2  =  0

So, the general equation of the required line is

5x - y - 2  =  0

3. Answer :

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 substitute 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 substitute 95 for x in

y  =  1500x + 100000

Then, 

y  =  1500x95 + 100000

y  =  142500  +  100000

y  =  242500

So, the cost of 95 units is $242500.

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