Question

spiral review

1. the table gives the altitude, y, of a weather balloon, in meters, at various times, x, in minutes, since the balloon was released from a platform. construct a function of the form $y = mx + b$ that describes the data.

time (x)	altitude (y)
4	220
5	270

Explanation:

Step1: Calculate slope $m$

First, use two points from the table, e.g., $(3,170)$ and $(4,220)$. The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$.
$m=\frac{220-170}{4-3}=\frac{50}{1}=50$

Step2: Solve for y-intercept $b$

Substitute $m=50$, $x=3$, $y=170$ into $y=mx+b$.
$170=50(3)+b$
$170=150+b$
$b=170-150=20$

Step3: Form the linear function

Combine the calculated $m$ and $b$ into $y=mx+b$.
$y=50x+20$

Answer:

$y=50x+20$