Question

if 15 sports jerseys cost $295 And 25 jerseys cost $425 write a linear equation that gives the cost C in dollars for J jerseys

Answer 1

Given that 15 sports costs $295 and 25 jerseys cost $425

To find the linear equation that gives the cost C in dollars for j jerseys

The fomula to find the linear equation is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Where y is the cost C and x is j jerseys

The coordinates are

`\begin{gathered} (x_1,y_1)\Rightarrow(15,295) \\ (x_2,y_2)\Rightarrow(25,425)_{} \end{gathered}`

Substitute the values into the formula above

`y-295=(425-295)/(25-15)(x-15)`

Solve to make y the subject,

`\begin{gathered} y-295=(425-295)/(25-15)(x-15) \\ y-295=(130)/(10)(x-15) \\ y-295=13(x-15) \\ y-295=13x-195 \\ Make\text{ y the subject} \\ y=13x-195+295 \\ y=13x+100 \end{gathered}`

Recall that, y = C and x = j, Substitute for y and x into the equation above

`C=13j+100`

Hence, the linear equation that gives the cost C in dollars for j jerseys is

`C=13j+100`