## Applied Linear Equations 2 - Sample Math Practice Problems

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### Complexity=1, Mode=perp-m

 1.   What slope is perpendicular to slope 1? 2.   What slope is perpendicular to slope 1/5?

### Complexity=1, Mode=para-perp

Determine if the lines are parallel, perpendicular, or neither.
1.

- 4x - 5y = 0
The lines are:

2.

The lines are:

### Complexity=1, Mode=makeline

 1.   In slope-intercept form, write the equation of the line that intersects (-2, -1) and is perpendicular to y - 1 = - 2x Equation: 2.   In slope-intercept form, write the equation of the line that intersects (5, -4) and is parallel to y - 2 = 2x Equation:

## Answers

### Complexity=1, Mode=perp-m

#ProblemCorrect AnswerYour Answer
1What slope is perpendicular to slope 1?
Solution
To calculate the perpendicular slope, flip it and reverse the sign.
1

Get the reciprocal
1

Reverse the sign
-1

#ProblemCorrect AnswerYour Answer
2What slope is perpendicular to slope 1/5?
Solution
To calculate the perpendicular slope, flip it and reverse the sign.
 15

Get the reciprocal
5

Reverse the sign
-5

### Complexity=1, Mode=para-perp

Determine if the lines are parallel, perpendicular, or neither.
#ProblemCorrect AnswerYour Answer
1

- 4x - 5y = 0
The lines are:

Solution
Slope analysis of

The equation is in point-slope form, y - y1=m(x - x1)
Therefore, the slope is -4/5

Slope analysis of - 4x - 5y = 0
The equation is in standard form, ax + by = c.
The slope is calculated as m = -a/b
Therefore, the slope is -4/5

The slopes are the same, so the lines are parallel.
#ProblemCorrect AnswerYour Answer
2

The lines are:

Solution
Slope analysis of

The equation is in point-slope form, y - y1=m(x - x1)
Therefore, the slope is -1/4

Slope analysis of

The equation is in point-slope form, y - y1=m(x - x1)
Therefore, the slope is 2/5

The slopes are not the same and don't multiply to -1, so the lines are neither parallel nor perpendicular.

### Complexity=1, Mode=makeline

#ProblemCorrect AnswerYour Answer
1In slope-intercept form, write the equation of the line that intersects (-2, -1) and is perpendicular to y - 1 = - 2x
Equation:
Solution
The slope of the line given is -2
The perpendicular slope is 1/2
With this perpendicular slope and intersection point, now derive the equation as you did in Applied Linear Equations 1.

#ProblemCorrect AnswerYour Answer
2In slope-intercept form, write the equation of the line that intersects (5, -4) and is parallel to y - 2 = 2x
Equation:
Solution
The slope of the line given is 2
Parallel lines have the same slope.
Given this slope and intersection point, now derive the equation as you did in Applied Linear Equations 1.
y = 2x - 14
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