Ryan is tracking how much money he has each week. He started with $60. He spent $5 per week for the first 6 weeks. He spent $10 per week after week 6 until the money's all spent.
what would the equation for the graph?
Let's break down the problem step by step:
- For the first 6 weeks, Ryan spent $5 per week. Therefore, his money decreased by $5 for each of the first 6 weeks.
- After the first 6 weeks, Ryan spent $10 per week until the money was all spent.
Let's denote the number of weeks as "x" and the amount of money Ryan has as "y". We can create the following equation to represent the situation:
If x ≤ 6, y = 60 - 5x
If x > 6, y = 60 - 5(6) - 10(x-6)
Simplifying the equation further:
If x ≤ 6, y = 60 - 5x
If x > 6, y = 30 - 10x
Therefore, the equation for the graph would be:
y = 60 - 5x, if x ≤ 6
y = 30 - 10x, if x > 6
is the graph linear or nonlinear?
The graph is linear in this case. Both equations, y = 60 - 5x and y = 30 - 10x, represent linear relationships between x and y. In both equations, the variable x is multiplied by a constant value (5 or 10) and then subtracted from a constant value (60 or 30), which is the slope-intercept form of a linear equation.
What is the y-intercept?
The y-intercept refers to the point where the graph intersects the y-axis. In this case, the y-intercept can be determined by evaluating the y-value when x is equal to 0.
For the equation y = 60 - 5x:
When x = 0, y = 60 - 5(0) = 60
So, the y-intercept is 60.
For the equation y = 30 - 10x:
When x = 0, y = 30 - 10(0) = 30
So, the y-intercept is 30.
Therefore, the y-intercept for both equations is 60.
what is the meaning of the y-intercept of this equation?
The y-intercept represents the value of y when x is equal to 0. In the context of this equation, the y-intercept of 60 means that originally, when the tracking started (at x = 0), Ryan had $60. This value represents the starting point or initial amount of money Ryan had before spending any money.
ok, in this equation what is the rate of change?
In the equation y = 60 - 5x, the rate of change can be determined from the coefficient of x, which is -5. This value represents the rate at which y changes for each unit increase in x.
The rate of change of -5 means that for every increase of 1 in x, y decreases by 5 units. In this context, it represents the rate at which Ryan is spending money each week. He spends $5 per week, leading to a decrease of $5 in his total amount of money tracked (y) for every week passed (x increase by 1).
The equation 7x + 5y = 100 is in standard form. This form tells us the x and y intercepts easily. What are the x and y intercepts?
To find the x-intercept, we set y = 0 in the equation and solve for x:
7x + 5y = 100
7x + 5(0) = 100
7x = 100
x = 100 / 7
x ≈ 14.29
So, the x-intercept is approximately (14.29, 0).
To find the y-intercept, we set x = 0 in the equation and solve for y:
7x + 5y = 100
7(0) + 5y = 100
5y = 100
y = 100 / 5
y = 20
So, the y-intercept is (0, 20).