Writing Slope Intercept Equations

Writing Slope Intercept Equations

 $y\ =\ mx\ +\ b\$  

There are three ways we can write a linear equation

• Slope Intercept Form

   $y\ =\ mx\ +\ b$  

• Standard Form                                                         $Ax\ +\ By\ =\ C\ \ \ \ \$  

• Point Slope Form                                                                 $m\ =\ \frac{y_2-y_1}{x_2-x_1}$  

Today we will focus on the slope-intercept (or y-intercept) form

In the equation

 $y\ =\ mx\ +\ b$  
the  m represents the slope (rise over run) and
the b represents the y- intercept (where the line crosses the y-axis)
the x and y are the (x,y) of a point on the line.

Slope

 $m\left(pos\right)=\frac{rise\ \ \uparrow}{run\ \longrightarrow\ }\ \ or\ \ m\left(neg\right)=\frac{rise\ \ \uparrow}{run\ \ \longleftarrow}$  
 

Let's start with finding the slope of a line on a graph. Pick a starting point (where the graph goes through the grid lines). Locate a second point and draw a triangle by going up and right or left to the next point.  Count how many you went up (rise). Count how many right (pos run) or how many left (neg run).

Multiple Choice

Find the slope of the line shown.

• 3/4

• -3/4

• 4/3

• -4/3

Multiple Choice

Find the slope of the line shown.

• -2/3

• 2/3

• -3/2

• 3/2

Multiple Choice

Find the slope

• -5/7
• 7/5
• -7/5
• 5/7

y-intercept

Find the point where the graph passes through the y-axis

The y-intercept is the y value when x=0

(0, y)

For example, if the point where it crosses the y-axis is (0, -5) we would say the y-intercept is y= -5. Since the b is the y-intercept, if we put this in the slope-intercept form it would look like y =mx + (-5) or y=mx-5.

Multiple Choice

What is the y-intercept?

• 2
• 3
• 4
• -2

Multiple Choice

What is the y-intercept?

• -1
• 3
• -3
• -2

Multiple Choice

_{What is the y-intercept of the line?}

• b = 1/2

• b = 1

• b = -1/2

• b= -1

Multiple Choice

What does 'b" represent in y=mx+b

• y-intercept
• macaroni
• nothing
• slope

Multiple Choice

What is the y-intercept in the equation y=2x + 3?

• 2

• 3

• 5

• Cannot be Determined

Slope

Remember that m is the slope in the slope-intercept form

 $y\ =\ mx\ +\ b$  

Multiple Choice

What is the slope in the equation y=2x + 3?

• 2
• 3
• 5
• Cannot be Determined 

Multiple Choice

What does "m" represent in y=mx+b?

• y-intercept
• slope
• macaroni
• nothing

Multiple Choice

Determine the slope and y-intercept from the following equation:   y = 3/2x + 3

• slope: 5   y-intercept:  (0,3) 
• slope: 3/2   y-intercept:  (0,3) 
• slope:  4  y-intercept:  (0,3/2)
• slope: 1/5   y-intercept:  (0,5) 

 $y\ =\ mx\ +\ b$  

Use the slope-intercept form

Given a slope of 3/4 and a y-intercept of 4, write the equation.
So m=3/4 and b=4 therefore
 $y\ =\ \frac{3}{4}x\ +\ 4$  

Multiple Choice

What is the equation of a line with m = 0 and b = 6

• y = 6

• y = 6x

• y = 0

• y = x

Multiple Choice

What is the equation of a line with m = -1 and b = 1/5

• y = -x + 1/5

• y = 1/5x - 1

• y = 1/5x + 1

• y = x + 1/5

Multiple Choice

What is the equation of a line with m = 6/5 and b = -5?

• y = 6/5x - 5

• y = 6/5x + 5

• y = -5x + 6/5

• y = 5x - 6/5

Multiple Choice

Which is the slope-intercept equation of the line with a slope of -2 and a y-intercept of 5?

• y = -2x + 5

• y = 5x - 2

• y = -2/5x + 5

• y = 2x - 5

Multiple Choice

Which is the slope-intercept equation of the line with a slope of 2/3 and a y-intercept of -2?

• y = 2/3x - 2

• y = -2x + 2/3

• y = -2/3x + 2

• y = 2/3x + 2