Question

1. mr. matthews is working at a new company where he will have to travel to meet with clients. the table below shows the relationship between the number of days mr. matthews has worked and the total number of miles he has traveled. use the table below to answer questions 17 - 18

days worked	4	6	11	17	27
miles traveled	122	183	?	518.5	829.5

write an equation to represent y, the total number of miles mr. matthews has traveled based on x number of days worked. type a response

Explanation:

Step1: Find the rate of change (slope)

The slope $m$ of a linear - relationship is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(4,122)$ and $(x_2,y_2)=(6,183)$. Then $m=\frac{183 - 122}{6 - 4}=\frac{61}{2}=30.5$.

Step2: Find the y - intercept (b)

We use the point - slope form $y=mx + b$ and substitute $m = 30.5$, $x = 4$, and $y = 122$. So, $122=30.5\times4+b$. Since $30.5\times4 = 122$, then $b = 0$.

Answer:

$y = 30.5x$