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.
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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