Question

a person travels by car. they record their miles driven in a data table.
using desmos, calculate the linear regression equation of this data.

time driving (hours)	0	1	2	3	4	5	6

$y = -1.79x + 61.93$
$y = 0.016x + 0.03$
$y = 61.93x - 1.79$
$y = 0.03x + 0.016$

Explanation:

Step1: Define variables

Let $x$ = Time Driving (Hours), $y$ = Total Distance (Miles)

Step2: Identify linear regression form

Linear regression: $y = mx + b$, where $m$ = slope, $b$ = y-intercept

Step3: Calculate slope/ intercept

Using the data points $(0,0), (1,55), (2,120), (3,188), (4,252), (5,307), (6,366)$, the regression gives $m \approx 61.93$, $b \approx -1.79$

Step4: Form the equation

Substitute $m$ and $b$ into the linear form.

Answer:

$y = 61.93x - 1.79$