Slope and Y-intercept

Slope and Y-intercept

State Test Review

Slope-intercept Form

• y = mx + b

• m represents the slope

• b represents the y-intercept

• Example: y=3x+4

• m(slope)=3

• b(y-intercept)=4

Multiple Choice

What is the slope of y=4x-6

• -6

• 6

• 4

• -4

Multiple Choice

What is the y-intercept of y=1/2x+4

• 4

• 2

• 1/2

• -4

Multiple Choice

What is the correct m and b of the equation:

 $y=-\frac{7}{2}x-3$  

• m= $\frac{7}{2}$    b=3

• m= $-\frac{7}{2}$   b=3

• m=  $-\frac{7}{2}$   b=-3

• m= -3  b= $-\frac{7}{2}$  

Poll

How are we feeling?

• Got it!

• Still Lost!

Slope and Y-intercept

Table

Slope

Slope is simply the change in the vertical distance over the change in the horizontal distance.

 $slope=m=\frac{rise}{run}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$  

Slope Example

• Points: (-2,-4) (2,-2)

•  $m=\frac{y_2-y_1}{x_2-x_1}$  

•  $m=\frac{-2-\left(-4\right)}{2-\left(-2\right)}$  

•  $m=\frac{1}{2}$  

Multiple Choice

What is the slope given the points (15, 8) and (10, 7)?

• 5

• $-\frac{1}{5}$

• $\frac{1}{5}$

• -5

Multiple Choice

What is the slope given the points (-2,-1) and (4,3)

• $\frac{3}{2}$

• $\frac{4}{3}$

• $-\frac{2}{3}$

• $\frac{2}{3}$

Multiple Choice

What is the slope of the table?

• 3

• -3

•  $\frac{1}{3}$  

•  $-\frac{1}{3}$  

Y-intercept

Table/ Two Points

Y-intercept from two points

• Write an equation of the line that goes through the points (-2, 1) and (4, 2).

  To write an equation, you need two things:

  
  

• To write an equation, you need two things:
   slope (m) = $\frac{1}{6}$  
   y – intercept (b) =?

•  $2=\frac{1}{6}\left(4\right)+b$  

• b= $\frac{4}{3}$  

Multiple Choice

What is the y-intercept given these two points: (3, 7) and (5, 11)

• -1

• 1

• 3

• -3

Let's Review !

• Find the slope: $\ (3,7)\ and\ (5,11)$    $\frac{11-7}{5-3}=\frac{4}{2}=2$  
  

•  $Now\ we\ have\ y=2x+b$  

•  $Let's\ use\ (3,7)\ \ y=2x+b\ \ \ 7=2(3)+b$  

•  $7=6+b$  

•  $1=b$  

Multiple Choice

Find the equation of the line with the following points (4,5) and (8,7)

• $y=\frac{1}{2}x+3$

• $y=2x-3$

• $y=-\frac{1}{2}x+3$

• $y=3x+\frac{1}{2}$