Answer:
In summary, the true statements about the equation y = 15x + 225 are:
- It is a linear function.
- It has a slope of 15.
- It has an initial value of 225.
Explanation:
The equation y = 15x + 225 represents the relationship between the total cost, in dollars, y, to rent a banquet hall for a party and the number of people attending, x. Let's analyze each statement to determine which ones are true.
A. The y-intercept is 15.
This statement is false. The y-intercept is the value of y when x is equal to zero. In this equation, when x is zero, the equation becomes y = 15(0) + 225, which simplifies to y = 225. Therefore, the y-intercept is 225, not 15.
B. It is a linear function.
This statement is true. A linear function is a function that can be represented by a straight line on a graph. The equation y = 15x + 225 is in the form of y = mx + b, where m represents the slope and b represents the y-intercept. Since this equation can be graphed as a straight line, it is indeed a linear function.
C. It has a slope of 15.
This statement is true. In the equation y = 15x + 225, the coefficient of x (the number multiplied by x) is 15. This coefficient represents the slope of the line. Therefore, the slope of this equation is indeed 15.
D. It has an initial value of 225.
This statement is true. As mentioned earlier, the y-intercept represents the initial value of y when x is equal to zero. In this equation, the y-intercept is 225, which means that when no one attends the party (x = 0), the total cost will still be $225.
E. It has a slope of 225.
This statement is false. As mentioned earlier, the slope of this equation is determined by the coefficient of x, which in this case is 15. Therefore, the slope of this equation is 15, not 225.