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## Applied Linear Equations 2 - Sample Math Practice Problems

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

 1.   What slope is perpendicular to slope -2? 2.   What slope is perpendicular to slope -4/3?

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

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

1.

y - 2 = 3(x - 3)
The lines are:

2.
y - 2 = x
- 4x - y = 24
The lines are:

### Complexity=1, Mode=makeline

1.   In slope-intercept form, write the equation of the line that intersects (2, 1) and is parallel to

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

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

1What slope is perpendicular to slope -2?
Solution
To calculate the perpendicular slope, flip it and reverse the sign.
-2

Get the reciprocal
 - 12

Reverse the sign
 12

2What slope is perpendicular to slope -4/3?
Solution
To calculate the perpendicular slope, flip it and reverse the sign.
 - 43

Get the reciprocal
 - 34

Reverse the sign
 34

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

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

1

y - 2 = 3(x - 3)
The lines are:

Solution
Slope analysis of

The equation is in slope-intercept form, y = mx + b
Therefore, the slope is -1/3

Slope analysis of y - 2 = 3(x - 3)
The equation is in point-slope form, y - y1=m(x - x1)
Therefore, the slope is 3

-1/3 × 3 = -1, so the lines are perpendicular.
2
y - 2 = x
- 4x - y = 24
The lines are:

Solution
Slope analysis of y - 2 = x
The equation is in point-slope form, y - y1=m(x - x1)
Therefore, the slope is 1

Slope analysis of - 4x - y = 24
The equation is in standard form, ax + by = c.
The slope is calculated as m = -a/b
Therefore, the slope is -4

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

### Complexity=1, Mode=makeline

1In slope-intercept form, write the equation of the line that intersects (2, 1) and is parallel to

Equation:
Solution
The slope of the line given is -1/4
Parallel lines have the same slope.
Given this slope and intersection point, now derive the equation as you did in Applied Linear Equations 1.