SOLVING & GRAPHING LINEAR EQUATIONS Determine if an equation is linear Identify the domain and range USE YOUR CALCULATOR TO: Find the domain when given the range Find the range when given the domain Graph linear equations and inequalities.

To determine if an equation is LINEAR it must have a degree of ONE 5x + 2y = 7 3x2 + 2y = 4 1/x – 1/y = 2 3/5x = y 3/5 x = y y/2 = 2 How do you find DEGREE? Add the exponents of the variables for each monomial. What is ANY line that you graph made up of? A series of POINTS In this lesson, we are going to find those points and use them to graph the line.

BEFORE GRAPHING…….. CHECK YOUR CALCULATOR SETTINGS! CHECK WINDOW SETTINGS. Press ZOOM at the top of the calculator Choose option #6 ZStandard – this will give you a “standard” 10 x 10 window. NEXT CHECK PLOTS. Press Y= At the top of the graph, Plot1, Plot2, Plot3 should NOT be highlighted. If the are, arrow up and press enter then arrow back down to Y1. This will turn them off.

Solve each equation for the given domain, then graph. FIRST – Solve for “y” 2x – y = -3 if the domain is {-3, -1, 0, 1, 3} x y -3 -1 1 3 domain range -3 Select y= button on your calculator. Type equation into line labeled “Y1” “X” is located under 2nd, next to “alpha” Press 2nd then GRAPH Choose your answer from the appropriate column. Use arrow keys to scroll up and down to find numbers. 1 3 5 9

Let's graph it. List ordered pairs from the table. (-3, -3) (-1, 1) (0, 3) (1, 5) (3, 9) Graph the ordered pairs Now press “GRAPH” on the calc. to see if the lines match.

-3 3 6 12 Solve each equation for the given domain, then graph. -6 -4 Example 2 FIRST – Solve for “y” 2. 2x – 3y = 12 if the range is {-6, -4, -2, 0, 4} x y -6 -4 -2 4 domain range -3 Select y= button on your calculator. Type equation into line labeled “Y1” “X” is located under 2nd, next to “alpha” Press 2nd then GRAPH Choose your answer from the appropriate column. Use arrow keys to scroll up and down to find numbers. 3 6 12

Let's graph it. List ordered pairs from the table. (-3, -6) (0, - 4) (3, -2) (6, 0) (12, 4) Graph the ordered pairs Now press “GRAPH” on your calc. to see if the lines match.

-4 -1 -6 1 Name the domain OR the range, then graph the equation. 6 -3 Example 3 FIRST – Solve for “y” 3. 3x + y = -6 x y 6 -2 -3 -9 domain range -4 Select y= button on your calculator. Type equation into line labeled “Y1” “X” is located under 2nd, next to “alpha” Press 2nd then GRAPH Choose your answer from the appropriate column. Use arrow keys to scroll up and down to find numbers. -1 -6 1

Let's graph it. List ordered pairs from the table. (-4, 6) (-2, 0) (-1, -3) (0, -6) (1, -9) Graph the ordered pairs Now press “GRAPH” on the calc. to see if the lines match.

What about INEQUALITIES? Work everything exactly the same way. Pay attention to your inequality symbol when you are graphing. > draw a - - - - - - - - - < draw a - - - - - - - - - > draw a ___________ < draw a ___________ The Inequality symbols tell you which side of the line to shade. < and < tell you to shade BELOW the graphed line (the part BELOW where it crosses the y-axis. > and > tell you to shade ABOVE the graphed line (the part ABOVE where it crosses the y-axis.

Let’s look at the graphs for #1 and #2 < or > use ___________ Y-intercept * The symbol is < so that means to shade BELOW the line you graphed – below where it crosses the “y”-axis.

< or > use - - - - - - - - Graph < or > use - - - - - - - - * The symbol is > so that means to shade ABOVE the line you graphed – above where it crosses the “y”-axis. Y-intercept