Question

mariana has a cell phone plan that has a monthly charge plus a per text fee. the table shows mariana’s monthly bill for october, november, and december along with the number of texts she sent during these months.

month	number of texts	monthly bill (dollars)
november	118	40.90
december	200	45.00

stat 1
enter in number of text on the l₁
enter in monthly bill on the l₂
stat → calc 4
enter down thru calculate

determine the y-intercept from the table of values and write it as an ordered pair.
y-intercept = (□ , □)

Explanation:

Step1: Define the linear model

Let the number of texts be \( x \) and the monthly bill be \( y \). The linear equation is \( y = mx + b \), where \( m \) is the slope (per text fee) and \( b \) is the y - intercept (monthly charge).

Step2: Calculate the slope \( m \)

Using two points, say \((x_1,y_1)=(45, 37.25)\) and \((x_2,y_2)=(200, 45.00)\). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1}\)
\(m=\frac{45.00 - 37.25}{200 - 45}=\frac{7.75}{155}=0.05\)

Step3: Find the y - intercept \( b \)

Substitute \( x = 45\), \( y = 37.25\) and \( m = 0.05\) into \( y=mx + b\)
\(37.25=0.05\times45 + b\)
\(37.25 = 2.25+b\)
Subtract 2.25 from both sides: \(b=37.25 - 2.25=35\)

The y - intercept occurs when \( x = 0\) (since in the linear equation \( y=mx + b\), when \( x = 0\), \( y=b\)). So the ordered pair for the y - intercept is \((0, 35)\)

Answer:

\(y\)-intercept \(=(0, 35)\)