Respuesta :
The linear functions for this problem are given as follows:
13. y = 2x/3 + 8/3.
14. y = -3x + 5.
15. y = -1/3x - 2.
16. y = 5/4x - 1/4.
17. y = 7/4x + 19/2.
What is a linear function?
A linear function is modeled by the following rule:
y = mx + b
In which:
- m is the slope, which is the rate of change, that is, the change in y divided by the change in x.
- b is the y-intercept, which is the the value of y when the function crosses the x-axis, that is, when x = 0.
The slope is also related with parallel and perpendicular lines, as follows:
- If the lines are parallel, they have the same slope.
- If the lines are perpendicular, the multiplication of their slopes is of -1.
In item 13, the line in slope-intercept form is:
y = 2x/3.
The line we want to find is parallel, hence it has the same slope, that is:
y = 2x/3 + b.
When x = -1, y = 2, hence:
2 = -2/3 + b
b = 8/3.
Hence the line is:
y = 2x/3 + 8/3.
For item 14, the line is perpendicular to:
y = 1/3x + 4.
Hence the slope is found as follows:
1/3m = -1
m = -3.
Then:
y = -3x + b.
When x = 0, y = 5, hence b = 5 and the line is:
y = -3x + 5.
For item 15, the line is perpendicular to:
y = 3x + 4.
Then the slope is found as follows:
3m = -1
m = -1/3.
Then:
y = -1/3x + b.
When x = 0, y = -2, hence b = -2 and the line is:
y = -1/3x - 2.
For item 16, the line is perpendicular to:
y = 4 - 4/5x.
Then the slope is found as follows:
-4m/5 = -1
m = 5/4.
Hence:
y = 5/4x + b.
When x = 1, y = 1, hence:
1 = 5/4 + b
b = -1/4.
Then the line is:
y = 5/4x - 1/4.
For item 17, the line is perpendicular to:
y = 13/7 - 4/7x
Then the slope is found as follows:
-4m/7 = -1
m = 7/4.
Hence:
y = 7/4x + b.
When x = -2, y = 6, hence:
6 = -14/4 + b
b = 19/2.
Hence the line is given by:
y = 7/4x + 19/2.
More can be learned about linear functions at https://brainly.com/question/24808124
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