Question

1. The total monthly cost, y, for smartphone service depends

Answer 1

Answer:

$\textsf{slope}=\dfrac{1}{5}$

$\textsf{Equation}: \quad y=\dfrac{1}{5}x+40$

y-intercept = 40

Step-by-step explanation:

$\large \begin{array}{| c | c |}\cline{1-2} \sf Text\:Messages\: & \sf Cost (\ ) \\x& y \\\cline{1-2} 0 & 40.00\\\cline{1-2} 10 & 42.00\\\cline{1-2} 20 & 44.00\\\cline{1-2} 30 & 46.00\\\cline{1-2}\end{array}$

Take two ordered pairs from the table:

$\textsf{let}\:(x_1,y_1)=(0, 40)$

$\textsf{let}\:(x_2,y_2)=(10, 42)$

Substitute them into the slope formula and solve for m:

$\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{42-40}{10-0}=\dfrac{1}{5}$

Use the point-slope form of a linear equation with the found value of m and the point (0, 40):

$\implies y-y_1=m(x-x_1)$

$\implies y-40=\dfrac{1}{5}(x-0)$

$\implies y=\dfrac{1}{5}x+40$

Slope-intercept form of a linear equation:  $y=mx+b$

(where m is the slope and b is the y-intercept).

Comparing with the calculated equation:

y-intercept = 40

Answer 2

• (0,40)
• (10,42)
• (20,44)
• (30,46)

Slope

• m=42-40/10
• m=2)10
• m=1/5

Equation in point slope form

• y-40=1/5x
• y=1/5x+40

slope=1/5

y intercept=40