You are 9 miles away from home. you start biking home at a speed of 6 miles per hour.
a. write an equation. in standard form that represents your distance from home y after x hours.
b. find the y-intercept of the graph. what does this represent?
c. find the x-intercept of the graph. what does this represent?

The distance and speed are illustrations of linear equations

The standard form is The y-intercept is 9The x-intercept is 1.5

The given parameters are:

(a) The standard equation

Because the distance reduces with time, the equation is:

This gives

Add 6x to both sides

(b) The y-intercept

This is the initial distance away from home.

So, the y-intercept is 9

(c) The x-intercept

Set y to 0, to calculate the x-intercept

Divide both sides by 6

This is the initial time away from home.

So, the x-intercept is 1.5

Read more about linear equations at:

link

A) y=9-6x, standard form is ax+by=c so add 6x to both sides

6x+y=9

b)  from the first, we had it in slope intercept form, mx+b where b is the y-intercept.  y=-6x+9

So the y-intercept is the point (0,9) which represents the starting distance before you start biking.  You start being 9 miles from your house.

c)  The x intercept occurs when y=0 so:

y=9-6x, so if y=0

0=9-6x

6x=9

x=9/6

x=1.5

This represent the time when you will arrive home and the total time that has elapsed to get there.

Answer: 10pi

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

6hope this ! ! ’