Answer:
\(y=32x+80\)
Step-by-step explanation:
Givens
- An electrician charges $80 plues $32 per hour.
Now, according to the problem, the electrician charges initially $80, that's a constant, it's not related with the number hours, that means it's the initial condition, the constant term.
Then, he charges $32 per hour, that is, this charge depends on the number of hours, it's variable. In other words, it represents a ratio of change.
So, if we apply all this to an equation, it would be
\(y=mx+b\)
Where, \(m\) is the ratio of change, \(b\) is the initial condition (y-intercept), \(x\) is time and \(y\) is money.
Therefore, the equation which models this situation is
\(y=32x+80\)
The y-intercept is for \(x=0\)
\(y=32(0)+80=80\)
The x-intercept is for \(y=0\)
\(0=32x+80\\x=\frac{-80}{32}= -2.5\)
Observe that x-intercept is at (-2.5,0), which doesn't make sense to the problem, because time cannot be negative.
