Unit 4 Lesson 5.2: Standard Form

Unit 4 Lesson 5.2: Standard Form

Ax+By=C

Let’s recap from Thursday’s lesson...

• A, the number in front of x has to be a whole number and positive.

• B and C also have to be whole numbers, but can be negative or positive.

• Again, no. Fractions. At. All.

• Let’s try a few..

Multiple Choice

Is the following equation in Standard Form? $\frac{1}{6}x+4y=8$  

• Yes, nothing wrong here. 

• No, “A” is negative. 

• No, “A” is a fraction. 

• No, “A” is a fraction and negative. 

Multiple Choice

Is the following equation in Standard Form? $-8x+3y=-2$  

• Yes, nothing wrong here. 

• No, “A” is negative. 

• No, “A” is a fraction. 

• No, “A” is a fraction and negative. 

Multiple Choice

Is the following equation in Standard Form? $-\frac{4}{7}x–6y=3$  

• Yes, nothing wrong here. 

• No, “A” is negative. 

• No, “A” is a fraction. 

• No, “A” is a fraction and negative. 

Multiple Choice

Is the following equation in Standard Form? $x-2y=–3$  

• Yes, nothing wrong here. 

• No, “A” is negative. 

• No, “A” is a fraction. 

• No, “A” is a fraction and negative. 

We also discussed X & Y-intercepts

(Long Method)

• X-Intercept: (_,0): Plug 0 in for y, then divide.

• Y-Intercept: (0,_): Plug 0 in for x, then divide.

X & Y-Intercepts (Short Version)

• X-Intercept: throw out the “By” and solve the one step equation of: Ax=C

• Y-intercept: throw out the “Ax” and solve the one step equation of: By=C

Multiple Choice

What is the x intercept of the following equation? $3x+4y=12$  

• (0,3)

• (3, 0)

• (4,0)

• (0,4)

Multiple Choice

What is the y intercept of the following equation? $3x+4y=12$  

• (0,3)

• (3, 0)

• (4,0)

• (0,4)

New lesson Info NOW!

• When an equation is given in Standard form, you can actually solve for the slope.

•  $m=\frac{-A}{B}$  

• To use this formula, you have to know what the A, B, and C is of the equation. 

Multiple Choice

What is the A value in this Standard Form Equation? $45x-18y=15$  

• A=45

• A= -18

• A=15

• A= 18

Multiple Choice

What is the B value in this Standard Form Equation? $45x-18y=15$  

• B=45

• B= -18

• B=15

• B= 18

Multiple Choice

What is the C value in this Standard Form Equation? $45x-18y=15$  

• C=45

• C= -18

• C=15

• C= 18

Slope from Standard Form: $m=\frac{-A}{B}$   

• Example: Given the Standard Form Equation of:  $2x-6y=18$  

• Knowing A=2, B= -6, and C=18. (We don’t need C though.)

•  $m=\frac{-A}{B}=\frac{-\left(2\right)}{—6}=\frac{-2}{-6}=\frac{2}{6}=\frac{1}{3}$  

• You can see, after plugging in 2 and -6, we get the fraction of 2/6, which will reduce down to 1/3.

Multiple Choice

Given Standard Form, what is the slope? $7x+14y=3$  

• Cannot solve, not in Standard Form. 

• M= -2

• M= -1/2

• M= 3/14

Multiple Choice

Given Standard Form, what is the slope?

12x-4y=7

• Cannot solve, not in Standard Form.

• M= 3

• M= -3

• M= 1/3

Multiple Choice

Challenge!
Find the slope given in standard Form: $3x+\frac{1}{6}y=7$  

• M= 2

• M=-18

• M= 18

• Cannot solve, this is not in Standard Form.

Last new information for this lesson!

• You need to be able to transform an equation from Standard Form to Slope Intercept form.

•  $Ax+By=C\ \ \rightarrow\ \ y=mx+b$  

Given this equation in Standard form, rewrite it on Slope Intercept. 

 $6x+2y=8$  

• This will always require TWO STEPS!

• Step 1: Subtract the “Ax” term, here it is 6x. Subtract 6x from both sides.   $2y=-6x+8$  

• Step 2: Divide the “B” from both sides, here B=2. Therefore, divide 2 from both sides.  $y=\frac{-6x+8}{2}$  

• Don’t forget to simplify!

•  $y=-3x+4$  

One more example: Rewrite this equation in Slope Intercept Form.

 $4x-3y=6$  

• Step 1: Subtract 4x from both sides.

•  $-3y=-4x-6$  

• Step 2: Divide both sides by “-3”

•  $y=\frac{-4x-6}{-3}$  

• Simplify!!           $y=\frac{4}{3}x+6$  

Multiple Choice

Rewrite the following equation in Slope Intercept Form. $6x+3y=12$  

•  $y=-2x+4$  

•  $y=2x-4$  

•  $y=\frac{1}{2}x+3$  

Multiple Choice

Rewrite the following equation in Slope Intercept Form. $4x-5y=10$  

•  $y=4x+2$  

•  $y=\frac{4}{5}x-2$  

•  $y=-\frac{4}{5}x-2$  

Multiple Choice

Rewrite the following equation in Slope Intercept Form.
 $3x-2y=-8$  

•  $y=3x+4$   

•  $y=-\frac{2}{3}x-4$   

•  $y=\frac{3}{2}x+4$   

Multiple Choice

You have finished the lesson.

If your Quizizz Lesson score is less than 50%, you must complete the Lesson Check.

If your Quizizz Lesson Score is MORE than 50%, you may leave and start your homework. :)

Homework is U4L5 Standard Form Worksheet.

• Yes I understand to do the Lesson Check (maybe) & Homework at this time.

• I’m supposed to do what now...?

• No thanks Miss Gockley. I like having a 13% in your class. 😁