Look at the graph below carefully
Observe the results of shifting ={2}^{x}f(x)=2x
vertically:
The domain, (−∞,∞) remains unchanged.
When the function is shifted up 3 units to ={2}^{x}+3g(x)=2x +3:
The y-intercept shifts up 3 units to (0,4).
The asymptote shifts up 3 units to y=3y=3.
The range becomes (3,∞).
When the function is shifted down 3 units to ={2}^{x}-3h(x)=2 x −3:
The y-intercept shifts down 3 units to (0,−2).
The asymptote also shifts down 3 units to y=-3y=−3.
The range becomes (−3,∞).
A 2/3 (67%) chance, which is likely.
There are a total of 48 marbles. If you take out the white marbles, 32 out of the 48 total marbles are not white (32/48). Simplify the fraction and you get 2/3.
Option B:
The equation of a line is 
.
Solution:
Given data:
Line passing through the point (4, 12).
y-intercept of the line = –2
The equation of a line in slope-intercept form is
y = mx + c
where m is the slope and c is the y-intercept.
c = –2
Substitute c = –2 in slope-intercept form.
y = mx – 2 – – – – (1)
To find m, substitute (4, 12) in the above equation.
12 = m(4) – 2
12 = 4m – 2
Add 2 on both sides of the equation.
14 = 4m
Divide by 2 on both sides of the equation.
Slope = 
Substitute m value in equation (1), we get
The equation of a line is .
Hence Option B is the correct answer.
point 1 = ( -1 , 5 ) point 2 = ( 5 , -5 )
equation of a line: y = mx + b
Find Slope (m):
( 5 - (-5)) / (-1 - 5))
= 10 / -6
= -3 / 2
slope = -3/2
Find y-intercept (b):
y = mx + b
y = -3/2 * x + b
5 = -3/2 * -1 + b <-------------- use the x and y coordinate of one of the . points. I used point 1 ( -1 , 5 )
b = 7/2 or 3.5
Assemble:
y = -3/2 * x + 3.5
