Deriving and Graphing
y = mx + b
y = mx + b
Graph Y = 4X + 3
*see students answers
Rewrite this equation into Slope-Intercept Form:
2x+y=−5
y =-2x -5
Find the solution of the graph.
( -2,-4 )
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)
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
Rewrite this equation into Slope-Intercept Form:
3x−4y=8
y = 3/4x - 2
Graph the following systems of equations:
y = 2x + 3 and y = -1/2x - 2
What is the solution?
( -2,1 )
Tell whether the system of equations has one solution, no solution, or many solutions.
-x + 2y = 6
y = 1/2x - 3
A line passes through (0, 7) and (3, 13).
Write the equation in slope-intercept form.
Y = 2X + 7
What is the y-intercept from this equation:
5x+2y=−12
-6
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.
Solve the following linear system algebraically to determine the solution :
y = 4x - 3 and 2x + y = 3
( 1,1 )
Derive slope-intercept form from the graph.
Y = -1/2X + 5
Rewrite in slope-intercept form and identify the slope:
8x−2y=16
4/1
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 )
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