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
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Where y is the cost C and x is j jerseys
The coordinates are
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(15,295) \\ (x_2,y_2)\Rightarrow(25,425)_{} \end{gathered}[/tex]Substitute the values into the formula above
[tex]y-295=\frac{425-295}{25-15}(x-15)[/tex]Solve to make y the subject,
[tex]\begin{gathered} y-295=\frac{425-295}{25-15}(x-15) \\ y-295=\frac{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}[/tex]Recall that, y = C and x = j, Substitute for y and x into the equation above
[tex]C=13j+100[/tex]Hence, the linear equation that gives the cost C in dollars for j jerseys is
[tex]C=13j+100[/tex]