Grade 8 math lesson second quarter

• A linear inequality in two variables is an equation that can be written in one of the four forms: a x ± b y is greater than c, a x ± b y is less than c, a x ± b y is less than or equal to c, or a x ± b y is greater than or equal to c.
• In a linear inequality, the variables a, b, and c are real numbers and should not be equal to zero.
• The inequality 4x + 5y is greater than 20 has two solutions: (2, 5) and (-4, 6).
• The inequality 4x + 5y is greater than 20 can have many more solutions, as shown by the graph of the linear equation.
• The graph of the linear inequality 4x + 5y is greater than 20 is a half plane, which consists of the points whose coordinates satisfy the inequality.
• An ordered pair x y is a solution of a linear inequality if a true statement results when the variables in the inequality are replaced by the coordinates of the ordered pair.
• Solutions of a linear inequality can be determined by substituting the coordinates of an ordered pair into the inequality and checking if a true statement results.
• A linear inequality in two variables can be written in one of four forms: a greater than, a less than, greater than or equal to, or less than or equal to.
• Inequality is true if the resulting inequality is true, and the side that contains the test points on the other side of the boundary.
• In an example, two x minus y is less than or equal to four can be rewritten as an equation, two x minus y is equal to four.
• The equation can be solved and plotted to find the intercepts, which are x = 2 and y = 0.
• The coefficients a, b, and c in a linear inequality in two variables should be real numbers and a and b should not be equal to zero.
• The solution of a linear inequality in two variables is represented by an ordered pair (x, y).
• The y-intercept of a linear inequality is the point where the inequality crosses the y-axis.
• The intercept of a linear inequality is the point where the inequality crosses the y-axis.
• The x-intercept of a linear inequality is the point where the inequality crosses the x-axis.
• Graphing linear inequalities involves transforming the inequality into an equation, which can be done by substituting 'y' for '5'.
• The boundary line in a linear inequality is not part of the solution.
• The graph of a linear inequality in two variables is a half plane.
• A linear inequality in two variables can be a solid or broken line.
• If the inequality is less than or greater than, the line should be a broken line.
• If the inequality is equal to, the line should be a solid line.
• The boundary line in the graph of a linear inequality in two variables is determined by the inequality itself.
• The intercepts in a linear inequality in two variables can be determined by solving the equation obtained from the inequality.
• The intercepts in a linear inequality in two variables can also be determined by plotting and drawing the boundary line.
• The solution set of a linear inequality in two variables can be determined by deciding which half plane contains the solution.
• If possible, the origin should be used as the origin in the graph of a linear inequality in two variables.
• If the origin cannot be used as the origin in the graph of a linear inequality in two variables, a test point should be used.
• The equation 2x-y=4 can be graphed on a Cartesian plane.
• The y-intercept of the equation 2x-y=4 can be found by solving the equation for y.
• The equation 2x-y=4 can be rewritten as x-y=2.
• The equation y=-4 has no theta's, so the y-intercept is also equal to -4.
• The x-intercept of the equation 2x-y=4 is found by solving the equation for x.
• The equation 2x-y=4 can be graphed on a Cartesian plane.

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