Slope
. What is the definition of slope?
The measure of the steepness of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run).
What is the definition of the y-intercept?
What is the definition of the y-intercept?
What is the definition of an equation?
A mathematical statement that shows the equality between two expressions, typically separated by an equal sign.
What is a system of equations?
- A set of equations with multiple variables that are solved
What is the purpose of a graph?
What is a visual representation of data? Graphs are used to visually represent data and provide a clear understanding of patterns, trends, and relationships.
What is the formula to calculate slope?
What is "rise over run"? The formula for slope is (change in y)/(change in x).
What does the y-intercept represent?
The initial value or starting point of a linear equation or graph
What is the solution to an equation?
What are the values that make the equation true? The solution to an equation is the set of values that satisfy the equation.
What is the solution to a system of equations called?
What is the point of intersection? The solution to a system of equations is the point(s) where the equations intersect and satisfy all the given equations.
What are the two main types of graphs?
What are bar graphs and line graphs? Bar graphs are used to compare categorical data, while line graphs are used to show the relationship between two variables over time or continuous data.
What does a positive slope indicate?
What does an upward line represent? A positive slope indicates that as the x-values increase, the y-values also increase.
How is the y-intercept represented in an equation?
What is the value of "b" in the slope-intercept form? The equation y = mx + b represents the y-intercept as the value of "b".
What is a linear equation?
What type of equation has a degree of 1? A linear equation is an equation with a degree of 1, meaning the highest power of the variable is 1.
How many solutions can a system of equations have?
What are one, infinite, or none? A system of equations can have one unique solution, infinitely many solutions, or no solution at all.
What is the x-axis and y-axis in a graph?
What are the horizontal and vertical axes? The x-axis represents the independent variable, while the y-axis represents the dependent variable.
What does a negative slope indicate?
What does a downward line represent? A negative slope indicates that as the x-values increase, the y-values decrease.
What does a positive y-intercept indicate?
What does a line above the origin represent? A positive y-intercept indicates that the line intersects the y-axis above the origin.
What is a quadruple equation?
What type of equation has a degree of 2? A quadratic equation is an equation with a degree of 2, meaning the highest power of the variable is 2.
What is the graphical representation of a system of equations?
What is a set of intersecting lines? The graph representation of a system of equations is a set of lines on a coordinate plane that may intersect at one point, form parallel lines, or not intersect at all.
What is the intersection point of the x-axis and y-axis called?
What is the origin? The origin is the point (0,0) where the x-axis and y-axis intersect.
What does a slope of zero represent?
What is a horizontal line? A slope of zero indicates a horizontal line, where the y-values remain constant regardless of the change in x-values.
. What does a y-intercept of zero represent?
What is the point where the line crosses the origin? A y-intercept of zero means that the line passes through the origin (0,0).
What is the slope-intercept form of a linear equation?
What is the equation form y = mx + b called? The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
How can a system of equations be solved?
- What are substitution, elimination, or matrix methods? A system of equations can be solved using various methods such as substitution, elimination depending on the complex and preference of the problem solver.
What is the slope of a straight line on a graph?
What is the ratio of vertical change to horizontal change? The slope of a straight line on a graph represents the rate of change and is calculated as the ratio of the vertical change (rise) to the horizontal change (run).