Linear Relations week 1

Question 1

What is an ordered pair?

Answer 1

a point made up of an X value and a Y value. It is a pair of coordinated with direction to a specific location

Question 2

What is the first coordinate of an ordered pair?

Answer 2

X value (horizontal axis)

Question 3

What is the second coordinate of an ordered pair?

Answer 3

Y value (vertical axis)

Question 4

Why is each section in the coordinate plane called a quadrant?

Answer 4

Because there are 4 separate sections

Question 5

What is the name of the quadrant where both coordinates are negative? (-x,-y)

Answer 5

3rd quadrant

Question 6

What is the name of the quadrant where both coordinates are positive? (x,y)

Answer 6

1st quadrant

Question 7

What is the name of the quadrant where the first coordinate is negative, and the second is positive? (-x,y)

Answer 7

2nd quadrant

Question 8

What is the name of the quadrant where the first coordinate is positive, and the second is negative? (x,-y)

Answer 8

4th quadrant

Question 9

Must every coordinate belong to a quadrant?

Explain.

Answer 9

No. If they land on an axis, they’re called an axis intersect. (X,0) would be X intersect. (0,Y) would be Y intersect.

Question 10

What is the origin point?

Answer 10

The exact point at which the X axis and Y axis intersect. Numerical value: 0.

Question 11

Define the coordinate plane:

Answer 11

A two-dimensional plane formed by the intersection of a vertical line called y-axis and a horizontal line called x-axis. They are perpendicular lines that intersect at 0.

Question 12

Define perpendicular:

Answer 12

The relationship between two lines which intersect and form a right angle (90°)

Question 13

Which quadrant would (-x,y) fall in?

Answer 13

2nd quadrant

Question 14

Which quadrant would (x,y) fall in?

Answer 14

1st quadrant

Question 15

Which quadrant would (-x,-y) fall in?

Answer 15

3rd quadrant

Question 16

Which quadrant would (x,-y) fall in?

Answer 16

4th quadrant

Question 17

Define what a table of values represents:

Answer 17

A table of values is a table which lists the values of y, given the x values, for a given line

Question 18

What is the most common set of X values in a table of values?

Answer 18

-2, -1, 0,+ 1, +2

Question 19

What changes in the X values in a table of values when there is a fraction in an equation describing a line?
Give an example.

Answer 19

The X values must be changed to be divisible by the denominator of the fraction.
If the equation is y = 1/3x + 4, all X values must be divisible by 3; …-6, -3, 0, +3, +6…

Question 20

How do we calculate the first difference?

Answer 20

1. Start at the bottom of the pair

2. Subtract the bottom number from the top number and repeat

Question 21

What is the first difference of a data set?

Answer 21

It is a method used to evaluate whether or not a linear equation is linear or non-linear

Question 22

Can the X value influence whether or not a linear equation is linear or non-linear?
Explain.

Answer 22

Yes. If the X values aren’t changing at a constant rate/pattern, the relation cannot be linear

Question 23

What are the other terms used when calculating slope?

Answer 23

Slope, gradient, angle, incline, or slant

Question 24

Define slope:

Answer 24

The measure of the steepness of a line

Question 25

What is the formula for calculating a slope?

Answer 25

m = rise (Y value) / run (X value)
or
m = y(2) - y(1) / x(2) - x(1)

Question 26

What is the difference between a rise and a run?

Answer 26

A rise is the vertical distance, and represents the Y axis/value.
A run is the horizontal distance, and represents the X axis/value.

Question 27

Finish the sentence:

The larger the slope value…

Answer 27

… the steeper the line

Question 28

Finish the sentence:

When calculating a physical slope value we…

Answer 28

… convert the final answer (fraction) into a decimal, or percent

Question 29

Finish the sentence:

When calculating the slope of a line segment from coordinate points, we…

Answer 29

… keep the final answer as a fraction (in lowest terms)

Question 30

Does it matter which points we use to calculate the slope in a line segment? (graph)
Explain.

Answer 30

No. As long as the line segment is constant, we can use any two points to calculate slope, then reduce to lowest terms.

Question 31

A line segment rising (increasing) from left to right has a ______ slope

Answer 31

Positive

Question 32

A line segment falling (decreasing) from left to right has a ______ slope

Answer 32

Negative

Question 33

What is a zero slope?

Answer 33

When there is no incline (rise) at all.

m = 0 / run

Question 34

What is an undefined slope?

Answer 34

When the run length is unknown.

m = rise / 0

Question 35

What is the relationship between two parallel lines?

Answer 35

They both have the exact same slope value

Question 36

What is the relationship between two perpendicular lines?

Answer 36

They have negative reciprocal slopes. (opposite and flipped)