Question

Find the equation of a secant line containing the given points:(4,f(4)) and (7,f(7) for f(x)=8x-7
i know
y=8x-7

x=4...y=(32-7)

x=7...y=(56-7)

delta y=56 - 32=24

dy/dx=slope=8

but i don't know how to write the equation of the line

Answer 1

i am not sure but you need something higher than a 1 degree polynomial equation to do a secant line right?

Answer 2

@timo86m, not really. The secant line will just be the same as the given line.
The slope of the secant line is
\[\frac{f(7)-f(4)}{7-4}=\frac{49-25}{7-4}=\frac{24}{3}=8\]
Now, using the point-slope formula,
\[y-y_0=m(x-x_0),\text{ replacing $(x_0,y_0)$ with either }(7,49)\text{ or }(4,25).\]