Question

write a linear equation to represent the relationship between x and y.
amount of battery charge (%)
time (hours)

Explanation:

Step1: Identify two points

From the graph, when \( x = 0 \) (time = 0 hours), \( y = 30 \) (battery charge = 30%). Another point: when \( x = 6 \) hours, \( y = 0 \) (battery charge = 0%). So points are \((0, 30)\) and \((6, 0)\).

Step2: Calculate the slope (\(m\))

Slope formula: \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substitute \((x_1,y_1)=(0,30)\) and \((x_2,y_2)=(6,0)\):
\( m=\frac{0 - 30}{6 - 0}=\frac{-30}{6}=-5 \).

Step3: Determine the y-intercept (\(b\))

The y-intercept is the value of \( y \) when \( x = 0 \). From \((0, 30)\), \( b = 30 \).

Step4: Write the linear equation

Linear equation form: \( y = mx + b \). Substitute \( m = -5 \) and \( b = 30 \):
\( y=-5x + 30 \).

Answer:

\( y = -5x + 30 \)