A MANUFACTURER WILL SUPPLY 200 MOTORS PER MONTH WHEN THE PRICE IS $30 AND
300 PER MONTH WHEN THE PRICE IS $40. ASSUMING THE SUPPLY CURVE IS LINEAR, WRITE
ITS EQUATION AND PUT INTO y = mx + b FORM.

To write the equation of the supply curve in the form $ y = mx + b $, where $ y $ represents the number of motors supplied and $ x $ represents the price of the motors, we will use the information provided:

1. When the price is $30, the manufacturer supplies 200 motors. This gives the point $ (30, 200) $.
2. When the price is $40, the manufacturer supplies 300 motors. This gives the point $ (40, 300) $.

### Step 1: Calculate the slope ($m$)
The slope ($m$) of the supply curve is the rate of change of the number of motors supplied with respect to the price, calculated by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points $ (30, 200) $ and $ (40, 300) $:

\[
m = \frac{300 - 200}{40 - 30} = \frac{100}{10} = 10
\]

### Step 2: Write the equation in point-slope form
Now that we have the slope, we can use the point-slope form of the line equation to find the full equation. The point-slope form is:

\[
y - y_1 = m(x - x_1)
\]

Using the point $ (30, 200) $ and $ m = 10 $:

\[
y - 200 = 10(x - 30)
\]

### Step 3: Simplify to slope-intercept form
Now simplify the equation to the slope-intercept form $ y = mx + b $:

\[
y - 200 = 10x - 300
\]
\[
y = 10x - 300 + 200
\]
\[
y = 10x - 100
\]

Thus, the equation of the supply curve is:

\[
y = 10x - 100
\]

### Conclusion:
The equation of the supply curve is $ y = 10x - 100 $, where $ y $ is the number of motors supplied and $ x $ is the price of the motors.

---

Would you like further details or have any questions about this? Here are some related questions:

1. How would you find the supply at a price of $50?
2. What is the minimum price at which motors are supplied, according to this equation?
3. What happens to the supply when the price drops to $25?
4. How would the supply change if the slope of the curve were steeper?
5. Can you write an equation for a demand curve that intersects with this supply curve?

**Tip:** Always check for consistency in the given points when using a linear model to ensure accuracy!

A MANUFACTURER WILL SUPPLY 200 MOTORS PER MONTH WHEN THE PRICE IS $30 AND 300 PER MONTH WHEN THE PRICE IS $40. ASSUMING THE SUPPLY CURVE IS LINEAR, WRITE ITS EQUATION AND PUT INTO y = mx + b FORM.

Learn how to find the equation of a linear supply curve given the relationship between motor prices and supply quantities. This problem covers key algebraic concepts such as calculating the slope and writing linear equations in slope-intercept form. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation