Slope
Equation in point slope form
slope=1/5
y intercept=40
Answer:
[tex]\textsf{slope}=\dfrac{1}{5}[/tex]
[tex]\textsf{Equation}: \quad y=\dfrac{1}{5}x+40[/tex]
y-intercept = 40
Step-by-step explanation:
[tex]\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}[/tex]
Take two ordered pairs from the table:
[tex]\textsf{let}\:(x_1,y_1)=(0, 40)[/tex]
[tex]\textsf{let}\:(x_2,y_2)=(10, 42)[/tex]
Substitute them into the slope formula and solve for m:
[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{42-40}{10-0}=\dfrac{1}{5}[/tex]
Use the point-slope form of a linear equation with the found value of m and the point (0, 40):
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-40=\dfrac{1}{5}(x-0)[/tex]
[tex]\implies y=\dfrac{1}{5}x+40[/tex]
Slope-intercept form of a linear equation: [tex]y=mx+b[/tex]
(where m is the slope and b is the y-intercept).
Comparing with the calculated equation:
y-intercept = 40
