Find a slope intercept equation of the line which is Paralle

Find a slope intercept equation of the line which is: Parallel to y = 1/2 x + 5, passing through (-1, 6) Perpendicular to y = 3x - 6 passing through (2, -3). Compute the average rate of f(x) 1/x over [1, 5] Graph the function f(x) = 3|x + 4|-4. Find the zeros, x- and y-intercepts, if any exist. Determine the domain and the range of this function. From the graph, list the intervals on which the function is increasing, decreasing, and find the relative and absolute extrema, if they exist Sketch the graph of f(x) = {x^2 if x lessthanorequalto 0 2x if x > 0 And then graph the transformed functions a) 2f(2 - x) 2 - f(x)

Solution

Equation of straight line is given by:

(y - y1) = m*(x - x1)

y = mx + c

A.

given equation is :

y = -(1/2)x + 5

slope m = -1/2

Point = (-1, 6)

Since we need to find parallel line, slope will be same

(y - 6) = (-1/2)*(x - (-1))

2y - 12 = -x - 1

2y = -x + 11

B.

Given equation is :

y = 3x - 6

m = 3

for perpendicular line slope = m*m1 = -1

m1 = -1/m = -1/3

Point = (2, -3)

equation of line will be

(y + 3) = (-1/3)*(x - 2)

3y + 9 = -x + 2

3y = -x - 7

x + 3y + 7 = 0