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EM2 8.5.Vocab
| Term | Definition |
|---|---|
| solutions to a system of linear equations | a set of values that makes all equations in the system true when substituted, representing the point where the lines intersect on a graph |
| system of linear equations | is a set of two or more linear equations that share the same variables and describe the same real-world situation |
| graph of a linear equation | a straight line on the coordinate plane, representing the set of all (x, y) solution pairs for that equation, showing a constant rate of change (slope) |
| isolate | the process of manipulating an equation to get a specific variable or expression by itself on one side of the equals sign. |
| linear equation | a linear equation is a statement of equality where the highest power of any variable is 1 , representing a straight line on a graph, often in forms like y=mx+b, and its solution makes the equation true, like x=2 for 3x+4=x+8. |
| parallel lines | lines in the same plane that are always the same distance apart and never intersect |
| point-slope eqaution of a line | The point-slope form of a line is a way to write a linear equation, \(y-y_{1}=m(x-x_{1})\), where \(m\) is the slope and \((x_{1},y_{1})\) is a specific point on the line, allowing you to easily create the equation from a known slope and point |
| slope | slope is the constant rate of change (steepness) of a line, defined as the rise over run |
| slope-intercept equation of a line | The slope-intercept form of a line, crucial in Eureka Math Squared, is y = mx + b, where 'm' is the slope (steepness/rate of change) and 'b' is the y-intercept (where the line crosses the y-axis at (0, b)) |
| solution to a linear equation | the specific value (or set of values) for the variable that makes the equation a true statement |
| standard form of a linear equation | Ax + By = C, where A, B, and C are integers (constants), and x and y are variables, with A typically not negative |
| x-intercept | the point where a graph crosses the horizontal x-axis, meaning the y-coordinate is always zero |
| y-intercept | the point where a line crosses the vertical y-axis, representing the initial value or starting point, always having coordinates (0, b), where 'b' is that specific y-value; you find it by setting x=0 in any equation and solving for y. |
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