Let's solve this step-by-step while interpreting the given information.
1. Understand the Linear Equation:
The general form of a linear equation is:
[tex]\[
y = mx + b
\][/tex]
where:
- [tex]\(y\)[/tex] represents the value of the investment at any time [tex]\(x\)[/tex],
- [tex]\(m\)[/tex] is the slope of the line,
- [tex]\(b\)[/tex] is the y-intercept.
2. Given Information:
- The slope [tex]\(m\)[/tex] is positive.
- The y-intercept [tex]\(b\)[/tex] is 30,000.
3. Identifying the Initial Investment:
The y-intercept [tex]\(b\)[/tex] in the equation [tex]\( y = mx + b \)[/tex] represents the value of [tex]\(y\)[/tex] when [tex]\(x\)[/tex] is 0. This can be understood as the initial value of the investment before any time has passed (at [tex]\(x = 0\)[/tex]).
Since the y-intercept [tex]\(b\)[/tex] is 30,000, this means that:
[tex]\[
\text{Initial investment} = 30,000
\][/tex]
4. Determining Whether the Investment is Increasing or Decreasing:
- The slope [tex]\(m\)[/tex] determines how the investment value changes over time.
- A positive slope ([tex]\(m > 0\)[/tex]) indicates that as [tex]\(x\)[/tex] (representing time) increases, [tex]\(y\)[/tex] (the investment value) also increases.
Therefore, given that the slope is positive, the value of the investment is increasing over time.
So, based on the information provided:
- The initial investment is 30,000.
- The investment value is increasing over time.
