The table below represents a linear function f(x) and the equation represents a function g(x): x f(x) −1 −6 0 −3 1 0 g(x) g(x) = 4x − 5 part a: write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x). (6 points) part b: which function has a greater y-intercept? justify your answer. (4 points)

Alright
the points of f(x) are
(-1,-6)
(0,-3)
(1,0)

and g(x)=4x-5

A.
find f(x)'s slope
the slope of the line passing through the points (x1,y1) and (x2,y2) is
(y2-y1)/(x2-x1)
so 2 points are (0,-3) and (1,0), so the slope is (0-(-3))/(1-0)=(0+3)/(1)=3/1=3
the slope of f(x) is 3

g(x)'s slope
y=mx+b
m=slope
so, given
g(x)=4x-5
4 is the slope
g(x)'s slope is 4

B.
the y intercept is the value when x=0
for f(x)
remember: (x,y)
notice we have the point (0,-3)
so the y intercept of f(x) is y=-3

for g(x)
y=mx+b
b=y intercept
g(x)=4x-5
the y intercept of g(x) is y=-5

f(x) has the greater y intercept because -3>-5

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12