Final answer:
To find the equation of the secant line for the function y=7√x at x=4 and x=9, calculate the corresponding y-values, determine the slope from the two points obtained, and write the equation using the point-slope form.
Step-by-step explanation:
The student is asked to find the equation of the secant line to the curve y = 7√x at the points where x = 4 and x = 9. To find the secant line, we first calculate the y-values for these x-values by plugging them into the given equation. This provides us with two points on the curve: (4, 7√4) and (9, 7√9), which simplify to (4, 14) and (9, 21).
Next, we calculate the slope of the secant line, which is the change in y over the change in x, known as Δy/Δx. The slope (m) is thus calculated as (21 - 14) / (9 - 4) = 7 / 5 = 1.4.
Using one of the points and the slope, we can then write the equation of the line in point-slope form: y - y1 = m(x - x1), which gives us y - 14 = 1.4(x - 4). Simplifying this equation yields the final equation of the secant line. With rounding to four decimal places, this simplification results in the equation y = 1.4x + 8.4, which is the required secant line equation.