Question

in 2001, there were approximately 109 million households with a computer and internet access. in 2009, there were approximately 119 million households. let x represent the number of years since 2000 and y represent the number of households (in millions) with a computer and internet access. identify two points that represent the number of households with a computer and internet access for 2001 and 2009.\
\bigcirc (0, 109) and (9, 119)\
\bigcirc (0, 109) and (8, 119)\
\bigcirc (1, 109) and (8, 119)\
\bigcirc (1, 109) and (9, 119)\
\
write the equation of the line in slope - intercept form with a slope of - 3 that passes through (4, 0).

Explanation:

First Sub - Question (Identifying the two points)

1. For the year 2001: Since \(x\) represents the number of years since 2000, in 2001, \(x = 2001 - 2000=1\). The number of households \(y = 109\) million. So the point is \((1, 109)\).
2. For the year 2009: \(x=2009 - 2000 = 9\). The number of households \(y = 119\) million. So the point is \((9, 119)\).

1. The slope - intercept form of a line is \(y=mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
2. We know that the slope \(m=- 3\) and the line passes through the point \((x_1,y_1)=(4,0)\).
3. Substitute \(m = - 3\), \(x = 4\) and \(y = 0\) into the equation \(y=mx + b\):

• \(0=-3\times4 + b\)
• \(0=-12 + b\)

1. Solve for \(b\):

• Add 12 to both sides of the equation: \(b=12\).

1. Now that we know \(m=-3\) and \(b = 12\), the equation of the line in slope - intercept form is \(y=-3x + 12\).

Answer:

D. \((1, 109)\) and \((9, 119)\) (assuming the options are labeled A, B, C, D with D being \((1, 109)\) and \((9, 119)\))

Second Sub - Question (Equation of the line in slope - intercept form)