Question

a rock climber is rappelling straight down a cliff. the table below shows the linear relationship between the time x (in minutes) since the rock climber began his descent and their height y (in meters) above the ground.
time (minutes) 0 1 2 3
height (meters) 16 12 8 4
write a linear equation to represent the relationship between x and y.

Explanation:

Step1: Identify y-intercept (b)

When $x=0$, $y=16$, so $b=16$.

Step2: Calculate slope (m)

Choose two points, e.g., $(0,16)$ and $(1,12)$.
$m=\frac{12-16}{1-0}=-4$

Step3: Write linear equation

Use slope-intercept form $y=mx+b$.
Substitute $m=-4$ and $b=16$.

Answer:

$y=-4x+16$