Hi there!
For a line to be PARALLEL, it must contain the same slope.
The given line has a slope of 4, so we can use the point-slope formula to solve:

y1 = y-coordinate of given point
x1 = x-coordinate of given point
m = slope
Plug in the values:

Simplify:

Answer:
a. LK = 4√3, JL= 4√6
b. PQ = 10√3, RP = 5√3
Step-by-step explanation:
a. LK =4√3,
LK=KJ= 4√3
sin(45°) = opposite/hypotenuse
hypotenuse (JL)= opposite/sin 45° = 4√3/√2/2 = 8√3/√2 = 8√3√2/2 = 4√6
b.
cos 30° = adjacent/hypotenuse = QR/PQ = 15/PQ
cos 30° = 15/PQ
PQ = 15/cos 30° = 15/√3/2)= 30/√3 = 30√3/3 = 10√3
tan 30° = opposite/adjacent = RP/QR
√3/3 = RP/QR
√3/3 = RP/15
RP = √3*15/3 = 5√3
Answer: The graph is shifted to the right by 5 units and shifted up from the parent function.
Step-by-step explanation:
1. By definition, a parent function is the simplest form of a function.
2. You have the following parent function given in the problem:

2. The function g(x) is obtained from the function f(x)

Where the subtraction of 5 indicates the horizotanl shift to the left and the addition of 2 indicates the vertical shift up.
3. Therefore, keeping the information above on mind, you can conclude that the answer is: the graph is shifted to the right by 5 units and shifted up from the parent function.
The answer is you need to post a pic in order to give help