Linear Relations week 1 Flashcards
What is an ordered pair?
a point made up of an X value and a Y value. It is a pair of coordinated with direction to a specific location
What is the first coordinate of an ordered pair?
X value (horizontal axis)
What is the second coordinate of an ordered pair?
Y value (vertical axis)
Why is each section in the coordinate plane called a quadrant?
Because there are 4 separate sections
What is the name of the quadrant where both coordinates are negative? (-x,-y)
3rd quadrant
What is the name of the quadrant where both coordinates are positive? (x,y)
1st quadrant
What is the name of the quadrant where the first coordinate is negative, and the second is positive? (-x,y)
2nd quadrant
What is the name of the quadrant where the first coordinate is positive, and the second is negative? (x,-y)
4th quadrant
Must every coordinate belong to a quadrant?
Explain.
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.
What is the origin point?
The exact point at which the X axis and Y axis intersect. Numerical value: 0.
Define the coordinate plane:
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.
Define perpendicular:
The relationship between two lines which intersect and form a right angle (90°)
Which quadrant would (-x,y) fall in?
2nd quadrant
Which quadrant would (x,y) fall in?
1st quadrant
Which quadrant would (-x,-y) fall in?
3rd quadrant
Which quadrant would (x,-y) fall in?
4th quadrant
Define what a table of values represents:
A table of values is a table which lists the values of y, given the x values, for a given line
What is the most common set of X values in a table of values?
-2, -1, 0,+ 1, +2
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.
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…
How do we calculate the first difference?
- Start at the bottom of the pair
2. Subtract the bottom number from the top number and repeat
What is the first difference of a data set?
It is a method used to evaluate whether or not a linear equation is linear or non-linear
Can the X value influence whether or not a linear equation is linear or non-linear?
Explain.
Yes. If the X values aren’t changing at a constant rate/pattern, the relation cannot be linear
What are the other terms used when calculating slope?
Slope, gradient, angle, incline, or slant
Define slope:
The measure of the steepness of a line
What is the formula for calculating a slope?
m = rise (Y value) / run (X value)
or
m = y(2) - y(1) / x(2) - x(1)
What is the difference between a rise and a run?
A rise is the vertical distance, and represents the Y axis/value.
A run is the horizontal distance, and represents the X axis/value.
Finish the sentence:
The larger the slope value…
… the steeper the line
Finish the sentence:
When calculating a physical slope value we…
… convert the final answer (fraction) into a decimal, or percent
Finish the sentence:
When calculating the slope of a line segment from coordinate points, we…
… keep the final answer as a fraction (in lowest terms)
Does it matter which points we use to calculate the slope in a line segment? (graph)
Explain.
No. As long as the line segment is constant, we can use any two points to calculate slope, then reduce to lowest terms.
A line segment rising (increasing) from left to right has a ______ slope
Positive
A line segment falling (decreasing) from left to right has a ______ slope
Negative
What is a zero slope?
When there is no incline (rise) at all.
m = 0 / run
What is an undefined slope?
When the run length is unknown.
m = rise / 0
What is the relationship between two parallel lines?
They both have the exact same slope value
What is the relationship between two perpendicular lines?
They have negative reciprocal slopes. (opposite and flipped)
