Answer:
Step-by-step explanation:
We are given the table representing the cost for the number of letters to be printed on shirts.
As, we know that slope is given by [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].
So, taking any two points ( x,y ) from the table say ( 15,7 ) and ( 20,8.25 ), we find the slope.
i.e. [tex]m=\frac{8.25-7}{20-15}[/tex]
i.e. [tex]m=\frac{1.25}{5}[/tex]
i.e. [tex]m=\frac{1}{4}[/tex]
i.e. [tex]m=0.25[/tex]
So, the slope is 0.25.
Now, we substitute the value of the slope and the point ( 15,7 ) into the equation y = mx + b.
i.e. 7 = 0.25 × 15 + b
i.e. b = 7 - 0.25 × 15
i.e. b = 7 - 3.75
i.e. b = 3.25
So, the y-intercept is 3.25
Hence, the linear equation is given by y = 0.25x + 3.25.
We know that the company charges a flat fee and also charges amount per letter.
Since, y = 0.25x + 3.25 is the total cost charged for the letters.
This gives us that, the slope 0.25 represents the charge per letter and the y-intercept 3.25 represents the flat fee charged.
