Write an equation of the line that passes through the points P(4, -3) and Q(-2,

Question

Write an equation of the line that passes through the points P(4, -3) and Q(-2, 6). Here is the graph of y = f(x). a. Find a point on the graph where a tangent line has a negative slope and mark it with the letter A. b. Find a point on the graph where a tangent line has a slope of zero and mark it with the letter B. Here is the graph of y = g(x). State the following values. If a value does not exist, write DNE. a. g(-1) b. g(1) c. g(2) d. lim_x rightarrow 3 g(x) e. lim_x rightarrow 1 g(x) f. lim_x rightarrow infinity g(x) Let f(x) = x^2 - 2x. Simplify or evaluate the expressions: a. f(x - 1) b. f(3 + h) - f(3)/h, with h notequalto 0 A stone is tossed into the air from a rooftop. Its height (in feet) above the ground after t seconds is given by f(t) = -16t^2 + 60t + 32. a. Find the average velocity between t =1 and t = 3 sec. b. Complete the table below to make a conjecture about the instantaneous velocity at t = 2 sec. True or false? If lim_x rightarrow infinity f(x) exists, it always equals f(a). Justify your answer.

Explanation / Answer

1. P (4 , -3) and Q (-2 , 6)

the slope of the lne passing through the points P and Q is m = (6+3)/(-2-4) = -9/6 = -3/2

now lets use the point slope form : y-y1 = m(x-x1)

m = -3/2 and choose any one of the two given points lets choose P (4 , -3) as (x1,y1)

=> y + 3 = -3/2 * (x - 4)

y = -3x/2 + 3 ===> this is the required equation of the line

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.