Download 2.2 - HonorsPreCalTrig

2.2 Graphing Techniques: Linear Equations and Inequalities
SOLUTION- The solution of an equation, is made of 2 variables, which make an ordered
pair (x,y which can be plotted on a graph)
LINEAR EQUATION- When graphed, the equation is a straight line. The form used is
STANDARD FORM.
STANDARD FORM- Ax+By=C, the form in which linear inequalities are expressed (A
and B cannot equal 0)
STRAIGHT LINE- The outcome of a linear equation, when graphed on a set of axis
X-INTERCEPTS- The coordinates of the points in a graph which touch the x-axis.
Y-INTERCEPTS- The coordinates of the points in a graph which touch the y-axis.
LINEAR INEQUALITIES- inequalities in the form of Ax+By>C or Ax+By<C (with A,
B and C as real numbers).
COMBINED LINEAR INEQUALITIES- have the same properties as linear
inequalities, but are written as
TO GRAPH LINEAR EQUATIONS:
 Start by finding the x and y intercepts, by setting x and y equal to zero, and
solving for the variable. For x, plug in 0 for y and solve. For the y-intercept, plug
in 0 for x and solve for y.
 Take the x and y intercepts and plot them on the graph.
 Connect the two points with a straight line.
 You can check the accuracy of your graph by testing a point, and plugging in the
coordinates of the point into the original equation.
EX) Graph 4x+2y=4
1) Find x-intercepts. 4x+2(0)=4
4x=2 x=1/2
2) Find y-intercepts 4(0)+2y=4
2y=4 y=2
3) Plot points, connect with a straight line.
EX) Graph 3y= -6x
1) Find intercepts 3(0)= -6x x=0
3y= -6(0) y=0
If x & y both =0, the origin (0,0) is on the line.
2) Plot point at the origin. Because 3y= -6x, you can simplify and get y= -2x, which has a
slope of -2 (the line will go down).
If the slope and at least one point are known, you can plot more points.
3) Check your graph by testing point such as, (1,-2) 3(-2) = -6(1) -6 = -6
TO GRAPH LINEAR INEQUALITIES:
 Start by following the two steps above.
 Next, connect the intercepts with a line.
If the inequality has > or <, use a DASHED LINE
If the inequality has a > or <, use a SOLID LINE
 Check the accuracy of your line by testing a point on the line, and plugging in the
coordinates for x and y in the original equation.
 Notice the line separates the graph into two parts, above and below the line.
 Choose another test point that does NOT lie on the line, and substitute the
coordinates in for x and y. If the statement is true, shade the half in which the
point is located.
EX) Graph 2x- 1/2y > 4
1) Find intercepts and plot points, by using the steps in the above examples.
2) When graphing, use a SOLID line, because > means "greater then or equal to," so it
includes the line as a solution
3) Pick a test point, such as (1,2). If the statement proves true, shade the portion of the
graph containing that point.
EX) Graph x+3y< -6
1) Find Intercepts and plot points, by using the steps in the above examples.
2) When graphing, use a DASHED line, because < means "less then," so the line isn't
included as a solution.
3) Pick a test point, such as (0,0). If the statement proves true, shade the portion of the
graph cointaing that point.
Remember: If < or >, use a DASHED line
If < or >, use a SOLID line
Standard (Linear) Form: Ax+By=C
Standard (Inequality) Form: Ax+By < (or > or < or >) C