Given:
[tex]f(x)=3.5x^2-6x[/tex]
Line passes the point is:
[tex]x_{1\text{ }}and_{}\frac{\square}{\square}x_2[/tex][tex]\begin{gathered} x_1=5 \\ f(x_1)=3.5x^2_1-6x_1 \\ =3.5(5)^2-(6)5_{} \\ =87.5-30 \\ =57.5 \\ \text{ line pass=(5,57.5)} \end{gathered}[/tex][tex]\begin{gathered} x_2=10 \\ f(x_2)=3.5(10)^2-6(10)_{} \\ =350-60 \\ =290 \\ \end{gathered}[/tex]
line is y = mx+c
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} m=\frac{290-57.5}{10-5} \\ m=\frac{232.5}{5} \\ m=46.5 \end{gathered}[/tex]
Eq of line is:
y
[tex]\begin{gathered} y=46.5x+c \\ 290=46.5\times10+c \\ c=290-465 \\ c=-175 \end{gathered}[/tex]
So euation of line is:
[tex]\begin{gathered} y=mx+c \\ y=46.5x-175 \end{gathered}[/tex]
