Answer:
Part 1) [tex]y=x+21.5[/tex]
Part 2) [tex]y=x+18[/tex]
Step-by-step explanation:
Part 1) Write a linear equation that represents the cost of buying t-shirts from Paula's printing.
Let
x ----> the number of t-shirts
y ----> the cost in dollars
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take two points from the table
(2,23.5) and (4,25.5)
substitute in the formula
[tex]m=\frac{25.5-23.5}{4-2}[/tex]
[tex]m=\frac{2}{2}=1[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=1[/tex]
[tex](x1,y1)=(2,23.5)[/tex]
substitute
[tex]y-23.5=(1)(x-2)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
[tex]y=x-2+23.5[/tex]
[tex]y=x+21.5[/tex]
Part 2) Write a linear equation that represents the cost of buying t-shirts from Shantay's shirts.
Let
x ----> the number of t-shirts
y ----> the cost in dollars
step 1
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
take two points from the table
(2,20) and (4,22)
substitute in the formula
[tex]m=\frac{22-20}{4-2}[/tex]
[tex]m=\frac{2}{2}=1[/tex]
step 2
Find the equation of the line in point slope form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=1[/tex]
[tex](x1,y1)=(2,20)[/tex]
substitute
[tex]y-20=(1)(x-2)[/tex]
Convert to slope intercept form
[tex]y=mx+b[/tex]
[tex]y=x-2+20[/tex]
[tex]y=x+18[/tex]
