Writing Slope Intercept Form

Writing Slope Intercept Form

Poll

What does m stand for in  $y=mx+b$  

• magnitude

• slope

• y-intercept

• multiple

• point (x, y)

Poll

What does b stand for in  $y=mx+b$  

• balance

• slope

• point (x, y)

• binomial

• y-intercept

Slope Intercept Form

• m = slope

• +b = y-intercept

• y-intercept is a point (0, _ )

Multiple Select

Given the function: $y=4x$ 
What is the slope?

•  $\left(0,\ 4\right)$  

•  $4$  

•  $\frac{4}{1}$  

•  $4x$  

•  $0$  
  

Multiple Choice

Given the function: $y=4x$ 
What is the y-intercept?

•  $0$  

•  $none$  

•  $\left(0,\ 4\right)$  

•  $4x$  

•  $\left(0,\ 0\right)$  

Poll

TRUE or FALSE: $f\left(x\right)=4x$  is the same as  $y=4x$  

• TRUE

• FALSE

Multiple Select

Which of the following would represent the SLOPE INTERCEPT FORM for the line with the given information:

SLOPE = $3$  & Y-INTERCEPT =  $\left(0,\ 7\right)$  

•  $7=3\left(0\right)+b$  

•  $y=7x+3$  

•  $y=3x+7$  

•  $y=3\left(0\right)+7$  

•  $f\left(x\right)=3x+7$  

Multiple Select

Which of the following would represent the SLOPE INTERCEPT FORM for the line with the given information:

SLOPE = $-\frac{1}{4}$  & Y-INTERCEPT =  $\left(0,\ -2\right)$  

•  $y=-\frac{1}{4}x-2$  

•  $y=-\frac{1}{4}\left(0\right)-2$  

•  $f\left(x\right)=-\frac{1}{4}x-2$  

•  $y=-2x-\frac{1}{4}$  

•  $y=-\frac{1}{4}x+\left(-2\right)$  

Multiple Choice

What is the slope of this line?

• 
  

  $0$
  

• $\frac{3}{5}$

• $-\frac{3}{5}$

• $-\frac{5}{3}$

Multiple Choice

What is the y-intercept of this line?

• 
  

  $0$
  

•  $\left(-3,\ 5\right)$ 

•  $\left(0,\ 0\right)$ 

•  $none$ 

Equation in Slope Intercept Form

Can be any of the following:
 $y=-\frac{3}{5}x+0$  

 $y=-\frac{3}{5}x$  

 $f\left(x\right)=-\frac{3}{5}x$  

Multiple Select

Which of the following represents the equation in SLOPE INTERCEPT FORM for the given graph?

• $y=\frac{1}{4}x+4$

• $y=4x-1$

• $y=-4x-1$

• $y=-4x+4$

• $y=4x+4$

Fill in the Blank

Write the equation in SLOPE INTERCEPT FORM for the given graph. **DO NOT USE ANY SPACES!**

Multiple Choice

What would you do to $2x+y=7$  to get y by itself/solve for y?

• subtract 7 to both sides of the equation

• divide by 2 to the entire equation

• subtract y to both sides of the equation

• add 2x to both sides of the equation

• subtract 2x to both sides of the equation

Multiple Choice

Is  $y=-2x+7$   the same as  $y=7-2x$  ?

• YES

• NO

Rewriting into Slope-Intercept Form

• Subtract 2x

•  $y=7-2x$   is the same as  $y=-2x+7$  

• Slope = -2

• y-intercept = (0, 7)

Multiple Select

What would be your first step to "solve for y" for the equation:

 $5x+3y=3$  

• add 5x

• subtract 5x

• divide by 5

• combine 5x & 3y

• subtract 3

Rewriting into Slope-Intercept Form

• Subtract 5x

• Placing -5x in front of 3 sets up "general form of Slope-Intercept Form"

• Divide entire equation by 3

• Slope =  $-\frac{5}{3}$  
  

• y-intercept = (0, 1)

Multiple Select

What would be the first step to solve $x-2y=-4$  for y/get the equation into SLOPE INTERCEPT FORM?

• Subtract x on both sides to get: $-2y=-4-x$  

• Add 2y on both sides to get: $x=-4+2y$  

• Subtract x on both sides to get: $2y=-x-4$  

• Add x on both sides to get: $-2y=x-4$  

• Divide by 2 on both sides to get:
   $x-y=-2$ 

Rewriting into Slope-Intercept Form

• Subtract x

• Placing -x in front of -4 sets up "general form of Slope-Intercept Form"

• Divide entire equation by -2

• Slope =  $\frac{1}{2}$  
  

• y-intercept = (0, 2)

Example G - avoid forgetting negative in front of y

• Add 2y - now coefficient of y is POSITIVE!

• Add 4

• Divide entire equation by 2

• Slope =  $\frac{1}{2}$ 

• y-intercept = (0, 2)

• Different journey, same destination!

Give some practice problems a try!

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