Question

when kehlani left her house in the morning, her cell phone battery was partially charged. let b represent the charge remaining in kehlanis battery, as a percentage, t hours since kehlani left her house. a graph of b is shown below. write an equation for b then state the y - intercept of the graph and determine its interpretation in the context of the problem.
answer
b
the y - intercept of the function is which represents

Explanation:

Step1: Find the slope of the line

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((0,60)\) and \((9,0)\). Then \(m=\frac{0 - 60}{9-0}=\frac{-60}{9}=-\frac{20}{3}\)

Step2: Write the equation of the line

The slope - intercept form of a line is \(B = mt + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. We know \(m =-\frac{20}{3}\) and \(b = 60\) (from the point \((0,60)\)). So the equation is \(B=-\frac{20}{3}t + 60\)

Step3: Identify the \(y\) - intercept

The \(y\) - intercept occurs when \(t = 0\). In the equation \(B=-\frac{20}{3}t + 60\), when \(t = 0\), \(B = 60\)

Step4: Interpret the \(y\) - intercept

In the context of the problem, when \(t = 0\) (i.e., when Kehlani left her house), the battery charge \(B\) is \(60\%\)

Answer:

The equation for \(B\) is \(B =-\frac{20}{3}t+60\). The \(y\) - intercept of the function is \(60\), which represents the percentage charge of Kehlani's cell - phone battery when she left her house.