Kevin’s Cards about 7th and 8th Grade Math Flashcards
What is the solution to a linear equation in 2 variables
A solution to a linear equation in 2 variables is a point: (x,y) or ordered pair
How many solutions does a linear equation in two variables have
Linear equations in 2 variables have infinitely many solutions and each solution is a point that lies on the same line as all the other solutions
Ax + By = C is what equation
Ax + By = C is a linear equation in 2 variables
How do you find the solution to linear equations with 2 variables
To find solutions to linear equations, chose a value for x, substitute the value into the equation , and solve for y. Do the same thing to solve for x with y
What is the standard form of a linear equation
The standard form of a linear equation is: Ax + By = C, where A,B, and C are integers, A is positive and B is non-zero
What is the names of the point of where a line crosses the x-axis and y-axis
The x-intercept of a graph is the x-coordinate of the point where the line intersects the x-axis. The y-intercept is the y-coordinate of the point where the graph intersects the y-axis
What is a Proportional Relationship
Proportional Relationships are a special type of linear equation when the ratio between two quantities is constant, the quantities have a proportional relationship
Rate Definition
A ratio of two quantities measured in different units
In a proportional relationship between two variables increases at a constant what
In a proportional relationship between two variables increases at a constant rate (also called a unit rate) as the other variable increases by one
Ratio Definition
A comparison of two quantities by division
A proportional relationship can be modeled as what
y = mx
When is the slope (m) on a graph positive
The slope (m) is positive if the line rises from left to right
When is the slope (m) on a graph negative
The slope (m) is negative if the line falls from left to right
What is the slope (m) on a graph equal to 0
The slope (m)is equal to 0 when the line is horizontal
What is a slope
The slope of a line is the ratio of the vertical change between any two point on the line to the horizontal change
What is another name for the vertical change and the horizontal change of a line’s slope
The vertical change is called the rise and the horizontal change is call the run
What is the format for the equation for slope
Vertical change/ Horizontal change or Rise/ Run
What directions do you move when moving in a positive or negative direction on a graph
When you move up or right you move in a positive direction. When you move down or left, you move in a negative direction
What is the Formula for Slope
y2 - y1/ x2 - x1
What is the slope of a vertical line on a graph
A slope is undefined if the line is vertical
What is a hypotenuse
The hypotenuse of a right triangle is the longest side of the triangle which is always opposite of the right angle (90 degrees)
Any two points on a line are what
Any two points on a line are the end points of a segment that, together with the rise and run, form a right triangle
What can the slope of the line tell you about the rate
The greater the slope of the line, the greater the rate. So when you compare lines, the line with the greater slope has the greater rate
What does the steepness of a line on a graph tell you
The steeper the line, the greater the slope
Each form of a linear equation communicates what
Each form quickly communicates specific information
What is the point - slope form of a line useful for
Communicating the slope of a line and one-point on the line
What is Point Slope Form
y - y1 = m(x - x1)
If a number is added in point-slope form what sign is it
It is negative
A proportional relationship can be modeled as what
y = mx
When a graph intersects the origin, you can do what to find the slope
Use any point to find the slope
What is slope-intercept form
y = mx + b, where b the y-intercept and m is the slope
Rate Definition
A ratio that compares quantities of a different kinds of units
Unit Rate Definition
A rate in which the 2nd quantity is 1
Terminating Decimals Definition
Decimals that have a finite number of nonzero digits
Initial Value Definition
The beginning value of a linear relationship; y-intercept
Ratio Definition
The relationship between two or more quantities
Mph is and example of what
An unit rate
Two or more linear equations using the same variables make up what
A system of linear equations
What is the solution of a system of linear equations
A solution of a system of linear equations is a point where the lines of the equations intersect
What does percent mean
Per 100
How do you convert a fraction to a percent
Multiply by 100
How do you convert a percent to a fraction
Divide by 100
A system with at least one solution is a what
A consistent system
What is a system with exactly one solution called
A consistent independent system
The lines in a consistent independent system do what
They intersect at exactly one point and have different slopes
A system with infinitely many solutions is what
A consistent dependent or a coincident
The lines in a consistent dependent system is also called a what
Coincident
A system that has no solutions is what
Inconsistent
The lines in a inconsistent system are what
Parallel
What are the slopes and y-intercepts like in an inconsistent system
Same slopes and different intercepts
What are the slopes and y-intercepts like in a consistent dependent system
Same slopes and same y-intercepts
What are the slopes and y-intercepts like in a consistent independent system
Different slopes and different or same y-intercepts
Percent Error
The absolute value of the Estimated value - actual value divided by actual value times 100
What is Commission
Commission is a payment based on amount of sales an employee makes. It is usually calculated as a percent of the employee’s total. For this reason, the more sales an employee makes, the more money he or she makes. Many commission base companies/jobs also pay a base salary that guarantees that the employee will receive money even if there are no sales
Commission
Earning = base salary + (commission% x sales)
When putting your money in a bank what can you earn on it
You can earn interest on it
What is used to solve for simple interest
I = Prt, I: interest earned, P: principal, r: interest rate, and t: time in years
Interest Rate Definition
The percentage of the original amount of money on which on which the interest will be calculated
Principal Definition
Money that earns interest at a given rate over time; the principal is the original amount of money on which interest is based
Simple Interest Definition
Interest earned or paid only on the principal
Interest Definition
The cost of borrowing money or the amount earned by lending money
Annual Rate Definition
Something paid every year (once a year)
Proportion Definition
An equation stating that two ratios are equal
Relation Definition
A mapping from a set of inputs to a set outputs
What are the inputs
Any x-coordinate
What are the outputs
Any y-coordinate
What are different ways a relation can be shown
A relation can be shown in ordered pairs, a table, and arrow diagram, or graph
Domain Definition
In a relation, the set of allowable inputs (all x-coordinates)
Range Definition
The set of possible outputs (all y-coordinates)
When is the domain and range both the set of all real numbers
When a graph of a line that is not vertical or horizontal contains an infinite number of elements in both its range and its domain
What is k
The constant of proportionality
What is the equation for k
k = y/x
Function Definition
A relation in which every element of the domain is assigned to exactly one element of the range
If a x-value is repeated, is the relation a function
No
Vertical Line Test Definition
For any relation, if a vertical line intersects the graph more than once, the relation isn’t a function
Linear functions are most often written in what line form
Slope-intercept form
Linear functions are written in what form
Slope-intercept form
What is the general form of a proportional relationship
y = kx
What is another for the constant of proportionality
Constant of variation
K can be everything but what
0
If in a linear equation written in slope-intercept form, has an exponent other than 1 over x, is it linear
No
Linear Function Definition
A function that when graphed forms a straight line
Nonlinear Function Definition
A function that when graphed doesn’t form a straight line
When describing Function graphs you must read from where to where
Left to right
When the x-values increases and the y-values increase, the line is what
Increasing
When the x-values increase but the y-values decrease, the line is what
Decreasing
When is a function constant
If the value of the function stays the same as x increases
What are key features when interpreting a function graph
Axis labels; the graph is increasing, decreasing, or constant; and if horizontal and vertical intercepts
Two-Way Table Definition
A table used to compare two categorical variables
Relative Frequency Table Definition
Table that describes the percent of occurrence of the values or intervals in a data set
What is frequency
How many times a value occurs
Categorical Variable Definition
A variable that is separable into mutually exclusive groups (For ex: boys and girls)
Cluster Definition
Points that are close together on a scatter-plot
What is an association
A pattern
What does Positive association mean
The points are rising
What does Negative association mean
The points are decreasing
What does no association mean
The pattern isn’t clear
How many solutions does a linear equation in one variable have
One
What is the sum of supplementary angles
180 degrees
Adjacent Angles Definition
Two angles in the same plane that have a common side and a common vertex, but no common interior points
Linear Pair Definition
Two angles that have a common side and the same vertex, and their other sides point in opposite directions
Vertical Angle Definition
The angles opposite of each other when two lines intersect to form 4 angles
What happens to the inequality sign when multiplying or dividing by negative numbers
The inequality sign gets reversed when you multiply and divide by negative numbers
Linear Inequality Definition
An inequality in which the variable is of degree one
How many angles are formed when a transversal goes through two parallel lines
8 angles
Alternate Interior Angles Definition
The inside angles on opposite diagonal sides of a transversal crossing two lines
Alternate Exterior Angles Definition
The outside angles on opposite diagonal sides of a transversal crossing two lines lines
Corresponding Angles Definition
Angles that lie in the same position or match up when a transversal intersects two lines
Transversal Definition
A line that intersects two or more lines in a plane
Corresponding Angles are what
Equivalent
Scale Factor Definition
The ratio of the side length of the image to the corresponding side length of the pre-image
Dilation Definition
A transformation that changes the size, but not the shape, of a figure
Enlargement Definition
A dilation that increases the size of a figure; the scale factor is greater than 1 in an enlargement
Reduction Definition
A dilation that reduces the size of a figure; the scale factor is less than 1 in reduction
In a triangle, how is an exterior angle formed
When a side of a triangle is extended
What does the exterior angle theorem state
“The measure of an exterior angle of a triangle is equal to the sun of the measures of the two no adjacent interior angles”
Equiangular Polygon Definition
A polygon with all angles congruent
Regular Polygon Definition
A polygon with all its sides congruent and all its angles congruent
