Which equation represents the linear function that is shown on the graph below? answers: y= 1/2x +4 y= 1/2x -2 y= 4x -2 y= -2x +4

Answer is choice B) y = 1/2x - 2

which is the same as y = (1/2)x - 2 or can be written as  

If you wanted the decimal form version, then the equation would be y = 0.5x - 2
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Explanation:

The four points on this line are 
(4,0)
(6,1)
(8,2)
(10,3)

Let's pick two of these points to find the slope.

The two points I'll pick are (4,0) and (6,1)

The first point is (4,0) so (x1,y1) = (4,0) meaning that
x1 = 4
y1 = 0

The second point is (6,1) so (x2,y2) = (6,1) meaning that
x2 = 6
y2 = 1

Using the slope formula, we find...
m = (y2 - y1)/(x2 - x1)
m = (1-0)/(6-4)
m = 1/2
m = 0.5

The slope in fraction form is 1/2. This means that each time we move up 1 unit, we move to the right 2 units. 
slope = rise/run = 1/2
Rise = 1
Run = 2

The fraction 1/2 is equivalent to the decimal form 0.5

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Let's use the slope m = 0.5, along with the point (x,y) = (4,0) to find the y intercept b

y = m*x + b
y = 0.5*x + b
0 = 0.5*4 + b
0 = 2 + b
0 - 2 = 2 + b - 2
-2 = b
b = -2
The y intercept is -2 meaning that the line crosses the vertical y axis at -2.

Therefore the equation is y = 0.5x - 2 after we update y = mx+b

This is the same as y = (1/2)x - 2 or y = 1/2x - 2 which is why choice B is the answer. The parenthesis help make it clear that x is not in the denominator; though technically they aren't needed. 

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