Outline for Linear Equations and Inequalities of 2 variablesSections 3.1-3.4A1. Substitute any value for x in the equation and solve for y. This results in a point (x, y). ORSubstitute any value for y in the equation and solve for x. This results in a point (x, y). 2. PLOT a minimum of 2 points (3 preferable) and connect with a line.B1. To find the x-intercept: Let y equal zero and solve for x.This point (x, 0) is the x-intercept, where the line crosses the x-axis.2. To find the y-intercept: Let x equal zero and solve for y.This point (0, y) is the y-intercept, where the line crosses the y-axis.3. If x = 0 when y = 0, then the origin is both the x-intercept and the y-intercept.4. Intercepts are often used as points to help graph a line.C1. If two points ),(11yxand ),(22yxare known, the slope can be found using the slope formula, 1212xxyym2. If the result is# nonzero0, the slope is 0.If the result is0# nonzero, the slope is undefined.D1. Solve the equation for y, bmxy form. The coefficient of the x term is the slope.2. If an equation has only a y variable, it is a horizontal line and the slope is 0.3. If an equation has only an x variable, it is a vertical line and the slope is undefined.Graphing a line by Plotting PointsFinding x and y interceptsFinding slope of a line from 2 given points1212xxyymFinding the slope from an equation of the lineE1. Solve the equation for y, bmxy form.2. The slope of the line is the coefficient of x and the point (0, b) is the y-intercept.3. If given the slope m and the y-intercept (0, b), substitute those number directly in this form.a) If the slope needs to be found first (from two points), use the slope formula.b) Note: If the point's x-coordinate is not zero, the y-coordinate isnot b. You must then use point-slope form.F1. Begin at the point given; for example, the y-intercept.2. Use rise over run to locate a second point on the line.a) If the slope is positive, move up numerator number of units, then right denominator number of units (or down then left).b) If the slope is negative, move down numerator number of units, then right denominator number of units (or up then left).G1. Substitute the slope of the line for m, the x coordinate of the point for 1x, and the y coordinate of the point for 1y.2. This form can be converted to slope-intercept form or standard form.H1. Always clear denominators (clear fractions) from the equation first by multiplying each term of the equation by the LCD.2. Move the terms with x and y to one side (x term in front) and the constant to the other side.3. If the x term coefficient if negative, multiply each term by -1 so A is positive.Slope-intercept form of an equation of a linebmxy Graphing a line using Slope and a PointPoint-Slope Form of an equation of a line,)(11xxmyy Standard Form of an equation of a line, CByAx A > 0, A, B, and C are integersI1. Positive Slope: line rises from left to right 2. Negative Slope: line falls from left to right 3. Zero Slope: line is horizontal 4. Undefined Slope: line is vertical J1. A vertical line through a point (k, h) has the equation x = k.(x = x-coordinate)2. A horizontal line through a point (h, k) has the equation y = k.(y = y-coordinate)K1. Parallel lines have the same slope. If dcdcm also is line parallelany of slope then the,2. Perpendicular lines have slopes that are opposite reciprocals.If cdmdcm then ,.L1. Convert the Inequality to slope-intercept form (if not already).2. If the inequality sign isor , make the line solid.If the inequality sign is < or >, make the line dashed.3. If the sign is or <, shade below the line.If the sign is or >, shade above the line.4. You can also use a 'test point' to determine which side to shade. If the original inequality is true after substituting x and y, shade that side.If the original inequality is false, shade the opposite side.4 types of SlopesEquations of Horizontal and Vertical Lineskykx and Slopes of Parallel and Perpendicular LinesGraphing a Linear
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