Question

tina flew in a hot air balloon and kept track of the height of the balloon as it ascended over time. which equation represents her results. (hint: put the data into a table and run a regression). y = 20x y = 3x + 60 y = 15x + 300 y = 20x + 60
time (minutes) height (feet)
3 60
6 120
9 180
12 240
15 300

Explanation:

Step1: Find the slope

The slope $m$ of a linear - equation $y = mx + b$ can be found using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say $(x_1,y_1)=(3,60)$ and $(x_2,y_2)=(6,120)$. Then $m=\frac{120 - 60}{6 - 3}=\frac{60}{3}=20$.

Step2: Check the y - intercept

For a linear equation $y=mx + b$, when $x = 0$, $y=b$. We can also note that when $x = 3,y = 60$. Substituting into $y=mx + b$ with $m = 20$ and $x = 3,y = 60$, we get $60=20\times3 + b$. Solving for $b$, we have $60 = 60 + b$, so $b = 0$. The equation of the line is $y=20x$.

Answer:

$y = 20x$