Question

It has been steadily snowing all day. Derek has been measuring the amount of snow in his yard. After 3 hours of snowing, he measures 6 inches of snow. After 7 hours, the amount of snow has increased to 14 inches. 1. Write an equation in point-slope form to represent this situation. 2. What does x represent in your equation? 3. What does y represent in our equation? 4. If the snow continues to fall, how much snow will there be after 24 hours?

Answer 1

We can imagine that x will be the number of hours and y will be the amount of snow. We can find the first-degree equation using the points (3,6) and (7,14) with the following equation:

$y-yo=m(x-xo)$

Let's find m first, we can do this using the following equation:

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$

y2 is 14, y1 is 6. x2 is 7 and x1 is 3. Thus:

$m\text{ = }\frac{14-6}{7-3}=2_{}_{}$

We can nominee the point (3,6) to be part of the xo, yo point in the first equation:

$y-6=2(x-3)$$y-6=2x-6$$y=\text{ 2x}$

If the snow continues to fall, after 24 hours (x), the amount of snow will be:

$y\text{ = 24}\times2=48\text{ inches}$