1.5.4 quick check review of graphing and systems of equation
Graphing:
1. In graphing, we plot points on a coordinate plane to represent numerical data or mathematical equations.
2. The x-axis represents the horizontal axis, and the y-axis represents the vertical axis.
3. To graph an equation, we plot points that satisfy the equation, and then connect the points to form a line or curve.
4. The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
Systems of Equations:
1. A system of equations involves multiple equations that are solved simultaneously to find the values of the variables that satisfy all the equations.
2. There are three possible solutions for a system of equations: a unique solution (a single point of intersection), infinitely many solutions (when the equations represent the same line), or no solution (parallel lines that do not intersect).
3. One method of solving systems of equations is by graphing. We graph each equation on the same coordinate plane and find the point of intersection, if it exists.
4. Another method is substitution, where we solve one equation for a variable and substitute it into the other equation. This allows us to solve for the remaining variable.
5. Elimination is another method, where we manipulate the equations to add or subtract them in order to eliminate one variable. This allows us to solve for the remaining variable.