Intercepts, Slope, & Slope-Intercept Form

Intercepts, Slope, & Slope-Intercept Form

How is this going to work?

• We're going to go through each topic

• Review how to figure out/calculate the answer

• Then practice for credit!

Intercepts

Lets practice finding x- and y-intercepts

Note about Intercepts:

They are usually written as ordered pairs: (x,y) but can also be written as x = or y = .

Finding Intercepts by Graph

Find the points when it crosses the x-axis (x-intercept) and y-axis (y-intercept)

Finding Intercepts Algebraically

Plug in zero for the other coordinate

Finding Intercepts Algebraically

Plug in zero for the other coordinate

Multiple Choice

What are the x- and y-intercepts on this graph?

• x-intercept = (0,5)

  y-intercept = (0,5)

• x-intercept = (5,0)

  y-intercept = (5,0)

• x-intercept = (5,0)

  y-intercept = (0,5)

• x-intercept = (0,0)

  y-intercept = (5,0)

Multiple Choice

What is the x-intercept of the line?

• $x=1$

• $x=2$
  

• $x=-1$
  

• $x=-2$
  

Multiple Choice

What is the y-intercept shown on the graph?

• $(0,-2)$

• $(3,0)$
  

• $(0,3)$
  

• None of these.

Multiple Choice

Find the x-intercept
 $4x+3y=24$  

•  $(6,0)$  

•  $(0,-6)$  

•  $(-8,0)$  

•  $(0,-8)$  

Multiple Choice

Find the y-intercept:
 $2y=8x+12$ 

•  $(0,6)$  

•  $(0,12)$  

•  $(0,\frac{4}{3})$  

•  $(0,\frac{1}{6})$  

Multiple Choice

What is the x-intercept?

• $\left(0,-3\right)$

• $\left(8,-1\right)$
  

• $\left(12,0\right)$

• $\left(16,1\right)$
  

Multiple Choice

What is the y-intercept?

•  $(0,7)$  

•  $(-2,3)$  
  

•  $\left(-1,5\right)$ 

•  $(-3.5,0)$  
  

Multiple Choice

What is the x-intercept in the equation  $x+2y=4$  ?

•  $\left(2,4\right)$ 

•  $\left(0,2\right)$ 

•  $\left(4,0\right)$ 

•  $\left(\frac{1}{2},0\right)$ 

Multiple Choice

 $y=-\frac{3}{5}x\ -30?$  

What is the y-intercept?

•  $\frac{3}{5}$  

•  $-30$ 

•  $30$  

•  $-\frac{3}{5}$  

Multiple Choice

 $y=3x+8$  

What is the y-intercept?

•  $\left(8,0\right)$ 

•  $\left(0,8\right)$ 

•  $\left(3,\ 0\right)$ 

•  $\left(0,3\right)$ 

Slope & Slope-Intercept Form

Slope-Intercept Form

A form of (way to write) linear equations, y=mx+b, where m is the slope and b is the y-intercept.

Slope

• A number that tells how steep the line will be.

• Slope is also called  $\frac{rise}{run}$  and is often written as a fraction. 

• The rise (top number /numerator) tells you how far to go up or down.

• The run (bottom number/denominator) tells you how far to go left or right.

• If the slope is a whole number, the run = 1.

• If the slope is positive, the graph will go up to the right (/). If it's negative, it will go down to the right(\).

Multiple Select

Which of the following equations are in slope-intercept form? (choose all that apply)

• $y\ =\ 4x\ +\ \left(-6\right)$

• $y\ =\ 4\ +\ 9x$

• $\frac{2}{9}x\ =\ y\ -3$

•  $y\ =\ x^{ }$ 

•  $y\ =\ -\frac{3}{6}x\ +\ 5$ 

Multiple Choice

In the equation y=mx+b, what does the m represent?

• slope

• y-intercept

• the first point

• x-intercept

Multiple Choice

 $y=-3x\ +\ 2$  

What is the slope?

•  $\frac{1}{3}$ 

•  $3$ 

•  $-3$ 

•  $2$ 

Multiple Choice

If m = 3 and b = 6, what is the correct slope-intercept equation?

• $y=3-6$

• $y=3x-6$
  

• $y=3x+6$
  

• $y=6x+3$
  

Multiple Choice

What is the equation of a line with a slope of 4 and a y-intercept (0,12) ?

•  $y=4x+12$  

•  $y=4x+0$  
  

•  $y=4x$  
  

•  $y=-4x-12$  
  

Multiple Choice

What type of slope does the following graph have?

• Postive

• Negative

• Zero Slope

• Undefined

Slope & Equations from a Graph

To determine slope from a linear graph, find two points, draw a triangle and calculate the rise/run.

To determine an equation from a graph, find the slope and the y-intercept and write the equation in slope-intercept form.

Multiple Choice

Find the slope of the line.

• -2
• 2
• -1
• 1

Multiple Choice

What is the equation of this line?

• $y=2x+2$

• $y=2x-2$
  

• $y=-x+2$
  

• Cannot be Determined

Multiple Choice

What is the equation of this line?

• $y=-3x-4$

• $y=-4x-3$
  

• $y=-\frac{3}{4}x-3$
  

• $y=-\frac{4}{3}x-3$
  

Multiple Choice

What is the equation of this line?

• $y=\frac{1}{3}x-1$

• $y=\frac{3}{2}x-1$
  

• $y=3x-1$

• $y=\frac{2}{3}x-1$