The graph shows y = 2x + 3
Explanation:
The graph is a straight line, with a slope of 2 and a y-intercept of 3. A linear equation is a function that has a constant slope, and the slope is defined as the change in y divided by the change in x. In this case, the change in y is 2 for every change in x of 1, so the slope is 2. The y-intercept is the value of y when x is 0, and in this case, the y-intercept is 3. So, the equation of the line is y = 2x + 3.
Applications:
The function y = 2x + 3 has many applications. For example, it can be used to:
- Calculate the total cost of a purchase, given the cost per item and the number of items purchased.
- Determine the distance traveled by a car, given the speed of the car and the time traveled.
- Predict the future value of an investment, given the initial value of the investment and the annual interest rate.
Real-World Examples:
Here are some real-world examples of how the function y = 2x + 3 can be used:
- A store charges $2 for each apple sold. The total cost of purchasing x apples is given by the function y = 2x + 3.
- A car travels at a speed of 60 miles per hour. The distance traveled by the car after x hours is given by the function y = 2x + 3.
- An investment earns an annual interest rate of 5%. The future value of the investment after x years is given by the function y = 2x + 3.
Conclusion:
The function y = 2x + 3 is a versatile function that has many applications in everyday life. It can be used to solve a wide variety of problems, from calculating the cost of a purchase to predicting the future value of an investment.