Let \( j \) represent John's age and \( s \) represent Sharon's age. According to the problem, we can set up the following equations:
- \( j = s - 4 \) (John is 4 years younger than Sharon)
- \( s = k \cdot j \) (Sharon is \( k \) times as old as John)
To express these equations in a standard form suitable for graphing, we can rearrange them:
-
Rearranging \( j = s - 4 \): \[ s = j + 4 \]
-
Rearranging \( s = k \cdot j \): \[ s - k \cdot j = 0 \text{ or } s = k j \]
Now you have the following two equations to graph:
- \( s = j + 4 \) (Equation for Sharon's age in terms of John's age)
- \( s = k j \) (Equation for Sharon's age in terms of John's age)
To graph these equations, you would:
-
For the first equation \( s = j + 4 \), plot the line with a y-intercept of 4 and a slope of 1. This means that for every 1-year increase in John's age, Sharon's age increases by 1 year.
-
For the second equation \( s = k j \), plot the line that passes through the origin (0,0) with a slope of \( k \).
The solution to the system of equations will be where the two lines intersect on the graph.
Without specific values for \( k \), I cannot draw or show a specific graph, but you can plot these lines based on the values you decide for \( k \) and find their intersection point for the solution.
If you have choices for graphs, look for the graph where the lines representing \( s = j + 4 \) and \( s = k j \) intersect, as that point will give you the ages of John and Sharon.
1 answer