Algebra: Chapter 9, Lesson 6, page 421.
Graphing Systems of Linear Inequalities
We continue Chapter 9-5 techniques and solve 2 inequalities.
For the first equation, we can use any technique we learned from Chapter 7. Usually, the slope-intercept or `x` and `y` intercepts can be used to quickly define the line. Check a simple point like (0, 0) to see if that part of the ½ plane is true. If so, then shade that area.
Do the same for the other inequality and shade the appropriate ½ plane. The IMPORTANT PART is WHERE THE 2 INEQUALITIES OVERLAP THEIR SHADING, IS THE SOLUTION TO BOTH INEQUALITIES.
Remember, boundary lines of the form `<` or `>` are DASHED. The line is NOT part of the solution. Lines of the form `≤` or`≥` are solid because their line ARE part of the solution.
Again, the textbook is pretty good here but here are some more examples from purplemath.com too!
Two of tonight’s homework problems solved by MrE are here! Just click it.
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Algebra 1a: Chapter 7, Lesson 3, page 313
Linear Equations and their Graphs
Linear equation have to have variables with a power of 1, NO mixed variable products and NO variables in an equation in the denominator. The easiest way to plot or graph an equation is to use the x-intercept and y-intercept.
- The x-intercept of a line is the x-coordinate of the point where the line intercepts the x-axis. To do this, all we have to do is set `y=0` and solve for `x`.
- The y-intercept of a line is the y-coordinate of the point where the line intercepts the y-axis. To do this, set `x=0` and solve for `y`
The standard form of a linear equation in 2 variables is `Ax + By = C`, where A, B and C are constants.
For horizontal lines, the graph of `y = b` is the x-axis or a line parallel to the x-axis with y-intercept, `b`.
For vertical lines. the graph of `x = a` is the y-axis or a line parallel to the y-axis with x-intercept, `a`.
Two of tonight’s homework problems solved by MrE are here! Just click it.