A linear equation is an equation with two variables whose graph is a line. The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation. If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern then connect the points to include all points. The easiest 2 points to plot are the x-intercept and the y-intercept.
- y = x + 2 - a straight 45 degree line rising from Quadrant III into Quadrant I, intersecting the y-axis at (2,0)
- Just solving for x = -1, 0, and 1 (y = 1, 2, 3) gives isolated points. This is an example of a discreet function.
- If you draw a line through all points and extend in both directions, you display a continuous function.
(https://www.mathplanet.com/education/pre-algebra/graphing-and-functions/linear-equations-in-the-coordinate-plane)
Graphing Inequalities
≤ and ≥ use a solid line, and < and > use a dotted line. Fill in above or below the line to represent the included values.
(https://www.mathplanet.com/education/pre-algebra/graphing-and-functions/graphing-linear-inequalities)
Systems of equations contain two or more equations.
(https://www.mathplanet.com/education/pre-algebra/graphing-and-functions/solve-systems-of-equations-by-graphing)