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Deriving and Graphing
y = mx + b
Standard Form
to
Slope-Intercept Form
Systems of
Linear Equations
Determining
Number of Solutions
100

Graph Y = 4X + 3

*see students answers

100

Rewrite this equation into Slope-Intercept Form:

 2x+y=−5

y =-2x -5

100

Find the solution of the graph. 

( -2,-4 )

100

One equation of a system of equations is y = 6x + 4. Write a second equation that would produce one solution.

 y = 7x + 3 (anything that has a different slope)

200

A line has a slope of −3/4 and passes through (0, –5).
Write the equation and identify whether the relationship is proportional.

 Y = -3/4X - 5

NON-PROPORTIONAL

200

Rewrite this equation into Slope-Intercept Form:

3x−4y=8

y = 3/4x - 2

200

Graph the following systems of equations:

y = 2x + 3     and      y = -1/2x - 2

What is the solution?

( -2,1 )

200

Tell whether the system of equations has one solution, no solution, or many solutions. 

-x + 2y = 6

y = 1/2x - 3

No Solution
300

A line passes through (0, 7) and (3, 13).
Write the equation in slope-intercept form.

Y = 2X + 7

300

What is the y-intercept from this equation:

5x+2y=−12

-6

300

Josh and Jordan are competing to see who will hit the most home runs this season. After 5 weeks, they will see who wins. Josh has already hit 15 before they started counting, and continues to hit 5 home runs every 2 weeks. Jordan has already hit 5 before they started counting, and continues to hit 5 home runs every week.

At what week will they hit the same amount of home runs? How many would each boy hit?

( 4,25 )

They will both hit 25 home runs in 4 weeks.

300

Solve the following linear system algebraically to determine the solution :

y = 4x - 3        and    2x + y = 3

( 1,1 )

400

Derive slope-intercept form from the graph. 

Y = -1/2X + 5

400

Rewrite in slope-intercept form and identify the slope:

8x−2y=16

4/1

400

Complete Each Table. For each equation, find the y-value for each x-value. What is the solution to the system of equations?

y = 2x +1.       and  y = x + 1

( 0,1 )

400

How can you tell just by looking at a system of equations how many solutions there will be?

One Solution :

No Solution :

Many Solutions : 

One Solution: They will have different slopes

No Solution: Same slope, different y-intercept

Many Solutions: Same slope, same y-intercept