As cell phones proliferate, the number of pay phones continues to drop. The number of pay phones from 2004 through 2009 (in millions) are shown below (x=0 corresponds to 2004) :

Question

As cell phones proliferate, the number of pay phones continues to drop. The number of pay phones from 2004 through 2009 (in millions) are shown below (x=0 corresponds to 2004) :

year,x : 0, 1, 2, 3, 4, 5
Number of pay phones: 1.30, 1.15, 1, 0.84, 0.69, 0.56

Derive an equation for the line.

So far I only found the slope m. Here is what I did:
0.56-1.30/5-0 = -0.74/5.

Would I proceed to find the y-intercept by using point-slope form?

Answer 1

Yes, you can find the equation of the line by using the point-slope form. Once you have the slope (m) that you calculated as -0.74/5, you can use any of the given points to find the equation of the line. Let's use the point (0, 1.30):

The point-slope form equation is:
y - y1 = m(x - x1)

Substituting the values from the point (0, 1.30):
y - 1.30 = (-0.74/5)(x - 0)

Simplifying:
y - 1.30 = (-0.74/5)x

To get the equation in the standard form (y = mx + b), you can rearrange the equation by adding 1.30 to both sides:
y = (-0.74/5)x + 1.30

Therefore, the equation of the line is y = (-0.74/5)x + 1.30.

Answer 2

To derive the equation for the line representing the number of payphones from 2004 to 2009, we will first calculate the slope using the given data points. You have correctly calculated the slope as -0.74/5.

To proceed in finding the equation of the line, you can use the point-slope form or the slope-intercept form of a linear equation.

Option 1: Using the point-slope form
The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) are the coordinates of any point on the line.

To use the point-slope form, you need to choose one of the data points. Let's pick the point (0, 1.30) since it corresponds to the year 2004.

Using this point and the calculated slope:
y - 1.30 = (-0.74/5)(x - 0)

Simplifying:
y - 1.30 = -0.148(x)

Option 2: Using the slope-intercept form
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

We have the slope as -0.74/5. To find the y-intercept, we need to find the value of y when x is 0. Using the point (0, 1.30):

y = (-0.74/5)(x) + b
1.30 = (-0.74/5)(0) + b
1.30 = b

Now we can write the equation in slope-intercept form:
y = (-0.74/5)(x) + 1.30

Both methods will give you the equation of the line representing the number of payphones as the years progress.

As cell phones proliferate, the number of pay phones continues to drop. The number of pay phones from 2004 through 2009 (in millions) are shown below (x=0 corresponds to 2004) :

yes

Yes, you can find the equation of the line by using the point-slope form. Once you have the slope (m) that you calculated as -0.74/5, you can use any of the given points to find the equation of the line. Let's use the point (0, 1.30):

To derive the equation for the line representing the number of payphones from 2004 to 2009, we will first calculate the slope using the given data points. You have correctly calculated the slope as -0.74/5.