Graphing Standard form linear equations

Standard form linear equations

By Alan Rabinowitz

What do you notice about the equation?

​ 3x + 4y = 24

​1) x and y are on the same side of the equal sign.

2) y is not by itself like slope intercept

3) there is a constant on the other side of the equal sign​

this is what a standard form equation looks like​

3x+4y=24

1) find y--it is not by itself

2) x and y are on the same side

3) we would like slope intercept when y is by itself ​to graph easier

​standard form

y = -3/4 x + 6

1) y is by itself.

2) this gives us the slope (-3/4)

and the y-intercept 6.

3) easy to graph​

​slope intercept

The difference between

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Let's do one​

​ 3x + 4y = 28

FIRST, FIND Y. IT IS WITH 3X, LET'S GET RID OF 3X BY SUBTRACTING 3X FROM BOTH SIDES SO 4Y IS BY ITSELF

​SECOND, DIVIDE BY THE NUMBER IN FRONT OF Y, SO DIVIDE BOTH SIDES OF THE EQUAL SIGN BY 4

​THIRD, SIMPLIFY

​

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​IT LOOKS LIKE THIS

3X + 4Y = 28

-3X -3X

​

4Y = 28 -3X

4 4 4​

Y = 7 - 3/4 X OR Y = -3/4 X + 7​

Subject | Subject

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Multiple Choice

Write in slope intercept form
5x - 3y = -9

• y = (5/3)x - 3
• y = (5/3)x + 9
• y = (5/3)x + 3
• y = (3/5)x + 3

Poll

HOW DO YOU FEEL ABOUT CONVERTING STANDARD FORM TO SLOPE INTERCEPT FORM?

• NOT GONNA LIE, STILL HAVING A HARD TIME

• I THINK I CAN GET SOME OF THE EASIER ONES

• I THINK I CAN BE SUCCESSFUL OF MOST

• I AM READY FOR THE MOST DIFFICULT PROBLEMS

​PRO TIPS

1) FIND Y AND THINK WHAT NEEDS TO BE DONE TO GET IT BY ITSELF

2) "DO WE HAVE A NEGATIVE Y" IF Y IS NEGATIVE, CHANGE ALL THE SIGNS FIRST. THIS MAKES THE DIVISION MUCH EASIER

3) IF IT HELPS YOU, PUT A "1" IN FRONT OF LETTERS THAT HAVE NO NUMBERS.

4) TRUST YOURSELF, BE CONFIDENT​

Subject | Subject

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Multiple Choice

YOUR TURN: CHANGE THIS STANDARD FORM EQUATION INTO A SLOPE INTERCEPT EQUATION

-4X + 5Y = 20

• $$X=5Y-20$$  

• $$Y=\frac{4}{5}X\ +20$$  

• $$Y=-\frac{4}{5}X\ +\ 4$$  

• $$Y\ =\ \frac{4}{5}X\ +4$$