Math Practice Problems - Applied Linear Equations 2

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Applied Linear Equations 2 - Sample Math Practice Problems

The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically graded and the difficulty adapts dynamically based on performance. Answers to these sample questions appear at the bottom of the page. This page does not grade your responses.

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Complexity=1, Mode=para-perp

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

Complexity=1, Mode=makeline

Answers

Complexity=1, Mode=perp-m

Problem

Correct Answer

Your Answer

What slope is perpendicular to slope -2?

Solution
To calculate the perpendicular slope, flip it and reverse the sign.
-2

Get the reciprocal

- 1
2

Reverse the sign

1
2

Problem

Correct Answer

Your Answer

What slope is perpendicular to slope -4/3?

Solution
To calculate the perpendicular slope, flip it and reverse the sign.

Get the reciprocal

- 3
4

Reverse the sign

3
4

Complexity=1, Mode=para-perp

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

Problem

Correct Answer

Your Answer

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.

#	Problem	Correct Answer	Your Answer
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

Problem

Correct Answer

Your Answer

In 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.

Problem

Correct Answer

Your Answer

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

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