For item a, the linear functions are given as follows:
1. y = 1.5x.
2. y = 0.5x - 1.
3. y = -0.5x + 1.
4. y = -1.5x - 1.
For item B, we have that:
1. The functions are:
a. y = 2x + 3.
b. y = 0.5x - 1.
2. The unit rates(slopes) are:
a. 2
b. 0.5.
What is a linear function?
A linear function is modeled by:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
- b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.
Item A
In graph 1, the function goes through (0,0), hence b = 0, and through point (2,3), hence the slope is:
m = (3 - 0)/(2 - 0) = 3/2 = 1.5.
Hence the function is:
y = 1.5x.
In graph 2, the function goes through (0,-1), hence b = -1, and through point (2,0), hence the slope is:
m = (0 - (-1))/(2 - 0) = 1/2 = 0.5.
Hence the function is:
y = 0.5x - 1.
In graph 3, the function goes through (0,1), hence b = 1, and through point (2,0), hence the slope is:
m = (0 - 1)/(2 - 0) = -1/2 = -0.5.
Hence the function is:
y = -0.5x + 1.
In graph 4, the function goes through (0,-1), hence b = -1, and through point (2,-4), hence the slope is:
m = (-1 - (-4))/(0 - 2) = -3/2 = -1.5.
Hence the function is:
y = -1.5x - 1.
Item B
In table a, the function goes through (0,3), hence b = 3, and through point (1,5), hence the slope is:
m = (5 - 3)/(1 - 0) = 2.
Hence:
y = 2x + 3.
The unit rate, which is the slope, is of 2.
For table b, the function goes through (2,0) and (6,2), hence the slope is:
m = (2 - 0)/(6 - 2) = 1/2 = 0.5.
Hence:
y = 0.5x + b.
When x = 2, y = 0, hence we can find b as follows.
0 = 0.5(2) + b
b = -1.
Thus:
y = 0.5x - 1.
The unit rate is of 0.5.
More can be learned about linear functions at https://brainly.com/question/24808124
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