Question

10 aniyah is driving home at a constant speed. after 20 minutes, she is 70 miles from home. after 1 hour, she is 40 miles from home. what equation models her distance from home, y, as a function of time, x? show your work.

Explanation:

Step1: Standardize time units

20 minutes = $\frac{20}{60} = \frac{1}{3}$ hours. Define $x$ (time) in hours, $y$ (distance from home) in miles. We have two points: $(\frac{1}{3}, 70)$ and $(1, 40)$.

Step2: Calculate slope (speed rate)

Slope $m$ = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{40 - 70}{1 - \frac{1}{3}} = \frac{-30}{\frac{2}{3}} = -45$

Step3: Find y-intercept (initial distance)

Use point $(1, 40)$ in $y = mx + b$:
$40 = -45(1) + b$
$b = 40 + 45 = 85$

Step4: Write linear equation

Substitute $m=-45$ and $b=85$ into $y=mx+b$.

Answer:

$y = -45x + 85$