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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?

Respuesta :

irspow
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.
MrRoyal

The distance and speed are illustrations of linear equations

  • The standard form is [tex]\mathbf{6x + y = 9}[/tex]
  • The y-intercept is 9
  • The x-intercept is 1.5

The given parameters are:

[tex]\mathbf{Rate = 6}[/tex]

[tex]\mathbf{Initial = 9}[/tex]

(a) The standard equation

Because the distance reduces with time, the equation is:

[tex]\mathbf{y = Initial-Rate \times x}[/tex]

This gives

[tex]\mathbf{y = 9 - 6\times x}[/tex]

[tex]\mathbf{y = 9 - 6x}[/tex]

Add 6x to both sides

[tex]\mathbf{6x + y = 9}[/tex]

(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

[tex]\mathbf{6x + y = 9}[/tex]

[tex]\mathbf{6x + 0 = 9}[/tex]

[tex]\mathbf{6x = 9}[/tex]

Divide both sides by 6

[tex]\mathbf{x = 1.5}[/tex]

This is the initial time away from home.

So, the x-intercept is 1.5

Read more about linear equations at:

https://brainly.com/question/11897796

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