Lesson 6-3 Standard Form of a Linear Equation

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Presentation transcript:

Lesson 6-3 Standard Form of a Linear Equation

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!

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.

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.

How to graph using Standard Form: Find the y-intercept. Find the x-intercept. Plug in zero for x. Ex. 2x + 3y = -2 2(0) + 3y = -2 0 + 3y = -2 3y = -2 y = -2/3 Plug in zero for y. Ex. 2x + 3y = -2 2x + 3(0) = -2 2x + 0 = -2 2x = -2 x = -1

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 or 2.6666666666 3(0) + 4y = 8 0 + 4y = 8 4y = 8 Y = 2 Now graph it! 

You try…Graph -4x + 3y = 12 X-int. (y=0) Y-int. (x=0) -4x = 12 Divide by -4 X = -3 3y = 12 Divide by 3 Y = 4 Now graph it! 

Weird Graphs y = 4 x = -2 Where does it cross the y-axis? Where does it cross the x-axis?

Classwork/Homework pg. 301 2-18 even, 23-26 all

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…

Convert Into Slope-Intercept Form (divide both sides by 2 to get y alone) (now simplify all fractions)

*** Check Your Answer *** -3y = -9x - 12 (divide both sides by -3 to get y alone) -3 -3 (now simplify all fractions) -3y = -9x - 12 -3 -3 -3 y = 3x + 4 Slope = 3 Intercept = 4

*** 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

Now you should be able to: Define standard form Define x- and y-intercepts Know how to solve the standard form of a linear equation for the x- and y-intercepts Graph using x- and y-intercepts Change standard form to y=mx+b form then graph the linear equation from there