Sarah has been running a dog-walking business since 2010. she walks dogs twice a day, takes them to the park, and returns them to their homes. each year, she has increased her fee by the same amount. the table shows what sarah charged each customer for two given years of her business: year annual dog-walking fee 2010 $350 2014 $750 a. what is the rate of change and initial value for sarah’s business? how do you know? b. write an equation in slope-intercept form to represent the fees that sarah charges each year.

Step-by-step explanation:if it's a linear equation

seems to be y=cost and x=years after 2010

so

find sllope

slope=change in cost/number of years

that is 750-350=change in cost=400

change in years is 2010-2014=4

so 400/4=100

y=100x+b

find b

started in 2010

she charged 350 initially

so that is 0 years after 2010

350=100(0)+b

350=b

so the equation is y=100x+350

A. rate of change is $100 per year, initial value is $350 becauuse it said so in the problem

B. equation is y=100x+350 if x is number of years after 2010

Read more on -

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."