Graphing in
Slope-Intercept Form
Slope-Intercept Form
Solve by graphing:
y = 2x + 2
y = x - 1
(-3, -4)
Leslie is opening a business to sell books. She sells each for $6, but it costs her $3 to print each book plus $24 in start up costs. Write the two equations for this system.
y = 6x
y = 3x + 24
y = - x + 5
What is the slope of an equation?
Rise / run, the rate of change, the "m" - value in the equation.
Solve by graphing:
y = 2x + 4
y = 3x + 2
(2, 8)
Julie and Mark are running a race. Julie starts at the 5 meter line and runs 4 meters per second. Mark starts at the starting line and runs 6 meters per second. Write the two equations that represent this system.
y = 4x + 5
y = 6x
Rewrite the following in slope-intercept form: x + 2y = 10
y = -1/2x + 5
What is the y-intercept of an equation?
Where the line crosses the y-axis, where x = 0, or by looking at the "b" -value in slope-intercept form.
Solve by graphing:
x = 2
y = 2x + 1
(2, 5)
Tom's parents are considering new phone plans. One plan charges an initial $50 fee plus $10 a line. The second plan has no initial fee but charges $20 a line. Write the two equations that represent this system.
y = 10x + 50
y = 20x
Rewrite the following in slope-intercept form: 4x + 2y = 20
y = -2x + 10
How can you tell the solution to a system of equations by looking at a graph?
The solution is where the two lines intersect.
Solve by graphing:
4x + 2y = 8
2x + y = 4
Infinite
David's family is getting new wifi service. One company offers a deal at $75 for the router plus $50 per month. Another company offers the router for $25 but charges $60 a month. Write the two equations that represent this system. Then create a table to show at what point the two companies would have charged the same total price.
y = 50x + 75
y = 60x + 25
After 5 months, both would have charged you $325.
Rewrite the following in slope-intercept form: 3x - 4y = 24
y = -3/4x - 6
If there is no solution to a system of equations, what do the two equations look like on a graph?
They will be parallel lines with the same slope.
Solve by graphing:
y = 1/2 x + 2
y = 1/4 x + 4
(8, 6)
Polly's Pizza Place charges $8 for their pizza plus $1 per topping. Jackie's Pizza charges $5 for their pizza plus $2 per topping. Write the two equations for this system. Then graph. How many toppings would you have to order at each place for the price to be equal?
y = x + 8
y = 2x + 5
They would have to order 3 toppings and would pay $11 for the pizza.
Rewrite the following in slope-intercept form: 5x - 3y = 18
y = 5/3x - 6
When two graphed lines are identical, how many solutions will the system have?
Infinitely many solutions