Answer:
[tex]y = 4.01\, x - 1.01[/tex].
Step-by-step explanation:
Overview of steps:
The secant line in this question intersects the given function at two points: [tex]x = 1[/tex], and [tex]x = 1 + 0.01 = 1.01[/tex]. The full coordinates of the two points are:
Since the secant line goes through the two points, the slope [tex]m[/tex] of this equation would be:
[tex]\begin{aligned}m &= \frac{(\text{rise})}{(\text{run})} \\ &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}} \\ &= \frac{3.0401 - 3}{1.01 - 1} \\ &= 4.01\end{aligned}[/tex].
The point-slope equation of this secant line would be:
[tex]y - y_{0} = m\, (x - x_{0})[/tex].
Using the point [tex](3,\, 1)[/tex]:
[tex]y - 3 = 4.01\, (x - 1)[/tex].
Simplify to obtain:
[tex]y = 4.01\, x - 1.01[/tex].
