2 What is Standard Form? Ax + By = C It’s when your x’s and y’s are on the same side equal to a number. Your x must be positive! x goes first!
3 Why do we have to know Standard Form? Standard Form is REALLY easy to graph is you use x- and y-intercepts.X-intercept is where the graph crosses the x-axis.Y-intercept is where the graph crosses the y-axis.
4 What are the coordinates? When something crosses the x-axis, what is the coordinate?(x, 0) The y is always zero.When something crosses the y-axis, what is the coordinate?(0,y) The x is always zero.
5 How to graph using Standard Form: Find the y-intercept.Find the x-intercept.Plug in zero for x.Ex. 2x + 3y = -22(0) + 3y = -20 + 3y = -23y = -2y = -2/3Plug in zero for y.Ex. 2x + 3y = -22x + 3(0) = -22x + 0 = -22x = -2x = -1
6 You try…Graph 3x + 4y = 8 X-int…plug in 0 for y Y-int…plug in 0 for x 3x + 4(0) = 8 3x + 0 = 8 3x = 8 X = 8/3 or3(0) + 4y = y = 8 4y = 8 Y = 2Now graph it!
7 You try…Graph -4x + 3y = 12 X-int. (y=0) Y-int. (x=0) -4x = 12 Divide by -4 X = -33y = 12 Divide by 3 Y = 4Now graph it!
8 Weird Graphs y = 4 x = -2 Where does it cross the y-axis? Where does it cross the x-axis?
10 It’s easier than you think… If you think this is confusing and you’re more comfortable with y=mx+b, then change standard to y=mx+b!It’s easier than you think…
11 Convert Into Slope-Intercept Form (divide both sides by 2 to get y alone)(now simplify all fractions)
12 *** Check Your Answer *** -3y = -9x - 12(divide both sides by -3 to get y alone)(now simplify all fractions)-3y = -9x - 12y = 3x + 4Slope = 3Intercept = 4
13 *** medium *** 21x – 7y =14 -7y = -21x + 14 y = 3x – 2 Convert to Slope-Intercept Form:21x – 7y =14(subtract both sides by 21x)(now divide both sides by -7)-7y = -21x + 14(simplify all fractions)y = 3x – 2
14 Now you should be able to: Define standard formDefine x- and y-interceptsKnow how to solve the standard form of a linear equation for the x- and y-interceptsGraph using x- and y-interceptsChange standard form to y=mx+b form then graph the linear equation from there