Question

a construction crew is lengthening a highway as part of a project. the length of the highway is recorded from when the project begins until it ends. the table below shows the linear relationship between the time x (in weeks) since the project began and the length y (in kilometers) of the highway.
time (weeks) | 0 | 1 | 2 | 3
length (kilometers) | 20 | 30 | 40 | 50
write a linear equation to represent the relationship between x and y.

Explanation:

Step1: Identify y-intercept (b)

When $x=0$, $y=20$, so $b=20$.

Step2: Calculate slope (m)

Choose two points, e.g., $(0,20)$ and $(1,30)$.
$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{30-20}{1-0} = 10$

Step3: Write linear equation

Use slope-intercept form $y=mx+b$.
Substitute $m=10$ and $b=20$: $y=10x+20$

Answer:

$y=10x+20$