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35 Cards in this Set
- Front
- Back
In the rectangular coordinate system: The horizontal line is called the:
The vertical line is called the: |
The horizontal line is called the: x - axis
The vertical line is called the: y - axis |
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What are the names for the quadrants in the rectangular coordinate system?
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starting with the upper right quadrant and moving counter-clockwise:
-first quadrant -second quadrant -third quadrant -fourth quadrant |
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The pair of numbers arranged in the order (x,y), which represent the x-values and y-values, are called:
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an ordered pair
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The x-value is called the:
The y-value is called the: |
The x-value is called the: x-coordinate or abscissa.
The y-value is called the: y-coordinate or the ordinate. |
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If a point is designated a label, say A, then as a matter of notation, that label may appear:
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in front of the coordinates, eg. if point A has coordinates (5,6), one may write: A(5,6).
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An equation with two variables is called a linear equation if:
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the exponent of each variable is 1.
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What does a linear equation look like when graphed on the x - y plane?
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a straight line, hence the name.
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What is the process for graphing a linear equation?
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1) Make two columns with x on one side and the equation where y is isolated on the other.
2) Place arbitrary values for x under the x column and substitute these values for x in the equation. 3) The result will be the value of y. Place this value under the y column. 4) Repeat for each arbitrary value. |
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The steepness of a linear equation is called the:
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slope
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The slope is measured by:
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the ratio of the Rise and the Run. ie. Rise / Run
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The Rise is:
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The Rise is the vertical difference between two points on the line. ie. Rise = y₂ - y₁
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The Run is:
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The Run is the horizontal difference between two points on the line. ie. Run = x₂ - x₁
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The Slope Formula:
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m = y₂ - y₁ / x₂ - x₁
Where m is used to designate the slope. |
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The Slope of a line is ascending if:
The Slope of a line is descending if: |
The Slope of a line is ascending if: it is going up from left to right. (the slope is positive)
The Slope of a line is descending if: it is falling from left to right. (the slope is negative) |
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If a Slope is "undefined," it means:
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that there is no slope. It will also be vertical. Vertical lines do not have slopes.
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All Horizontal lines have a slope of:
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zero
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What are the four different types of slopes?
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1) Positive slope: Line is ascending from left to right.
2) Negative slope: Line is descending from left to right. 3) No slope or "Undefined" slope: Line is vertical. 4) Zero slope: Line is horizontal. |
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What is the point-slope formula?
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y - y₁ = m(x - x₁)
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When is the point-slope formula used?
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When we want to find the equation of a line when a point on that line and the slope are given.
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In a linear equation, if the equation is expressed as y in terms of x ie:
y = 2x + 5 then the coefficient of x is always equal to: |
the value of the slope.
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In a linear equation, if the equation is expressed as y in terms of x ie:
y = 2x + 5 and we substitute 0 for x, then the value of y is always equal to: |
the constant term of the final equation ie. 5 in this equation. (if we substitute 0 for x, the constant is also the y-intercept)
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If, in an ordered pair, x = 0 then the point is on the ___ axis.
This point is called: |
y axis;
This point is called the y-intercept. |
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If, in an ordered pair, y = 0 then the point is on the ___ axis.
This point is called |
x axis;
This point is called the x-intercept. |
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What is the slope-intercept formula?
What formula is it a variation of? |
y = mx + b; where b = y-intercept.
It is a variation of the point-slope formula. |
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In the x-intercept, y =
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zero
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In the y-intercept, x =
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zero
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How do you find the x-intercept?
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Let y = 0 in the given equation and solve for x.
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How do you find the y-intercept?
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Let x = 0 in the given equation and solve for y.
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Vertical line formula:
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x = x₁
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Horizontal line formula:
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y = y₁
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Why is it very necessary to know the Vertical Line formula when trying to find the equation of a vertical line?
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Because vertical lines have a slope that is undefined. ie. zero as a denominator.
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How do you find the equation of a line if given two ordered pairs?
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1) Use the Slope formula to find the slope.
2) Use the Point-Slope formula to find the equation. |
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If all the ordered pairs in a line have the same x value then:
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the line is a vertical line.
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If all the ordered pairs in a line have the same y value then:
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the line is a horizontal line.
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What are the steps in order to graph an inequality in two variables?
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1) Replace the inequality with an "equals sign."
2) Solve for y, then graph the resulting equation. 3) If the original inequality includes "equal to" as well, ie. ≤ or ≥ then the graph is included in the solution. If the original inequality does not include an "equal," then a shaded line should be used to indicate that the graph is not part of the solution. 4) The graph obtained divides the plane into two regions called "half-planes." Pick two values that makes a point in one of the planes. Substitute these values into the original inequality. If it is true, then shade the plane on that side of the line. |