Question

1.6.8 stepping stones
the relationship between the number of hours a part - time employee works per day and the number of years since 2008 is shown in the graph.
what are the slope and the y - intercept of the line of best fit?
a m = - 0.35 and (0,0.22)
b m = - 0.35 and (0,0.9)
c m = 0.35 and (0,0.22)
d m = 0.35 and (0,0.9)

Explanation:

Step1: Identify two points on line

Choose two points on the line of best - fit, say $(0,0.9)$ and $(10,4.4)$.

Step2: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Substitute $x_1 = 0,y_1 = 0.9,x_2=10,y_2 = 4.4$ into the formula: $m=\frac{4.4 - 0.9}{10-0}=\frac{3.5}{10}=0.35$.

Step3: Determine the y - intercept

The y - intercept is the y - value when $x = 0$. From the point $(0,0.9)$, the y - intercept is $(0,0.9)$.

Answer:

$m = 0.35$ and $(0,0.9)$