Slope-Intercept
What is the equation for slope-intercept form?
y = mx + b
How do you know if a system of equations shows no solution on a graph?
Parallel lines
-3x + 4y = -2
y = -5
(-6, -5)
14x + 2y = 26
-14x - 6y = -50
(1, 6)
y = cost
Tonia gets the solution (7, 42) to a system of equations. What does her solution mean?
7 bracelets cost $42
If a proportional graph shows the point (4, 48) what is the slope of the line?
12
How do you know if a system shows infinite solutions on a graph?
Same line
-5x = 5y = 10
y = -4x - 17
(-5, 3)
2x + y = 7
x - 2y = 6
(4, -1)
A football team scores 7 times and earns 27 points with only 3-point field goals and 6-point touchdowns. Give a system of equations to solve this scenario.
x + y = 7
3x + 6y = 27
Jeremy starts 5 feet ahead of the starting line and swims at a rate of 3 meters per second. Given an equation modeled by this situation.
y = 3x + 5
Describe how to determine the solution of two graphed lines.
The point of intersection is the solution to the system.
y = -2x - 9
3x - 6y = 9
(-3, -3)
-15x + 6y = -36
8x - 6y = 22
(2, -1)
Give a system that models this situation. You don't need to solve.
You have 15 nickels and dimes. The coins are worth $1.20. How many of each coin do you have?
x + y = 15
0.05x + 0.10y = 1.20
What is a linear equation? Give an example.
A line that is straight when graphed; y = 2x
What kind of line is made by the equation x = 2?
vertical line (undefined slope)
-8x - 5y = -24
-x + y = 10
(-2, 8)
-3x - 24y = -66
3x + 4y = -14
(-10, 4)
Jackie runs and rides her bike. She runs 6 miles in an hour. She bikes 18 miles in an hour. Last week she ran and biked a total of 216 miles. It took her 16 hours. How many hours did Jackie run and bike last week?
6 hours running
10 hours biking
Convert the equation to slope-intercept form.
-9x - y = 2
y = -9x - 2
Graph the system and show the solution.
y = 1/4x - 2
y = 3/2x + 3
(-4, -3)
-8x + y = -7
16x - 2y = 14
Infinitely many solutions
3x + y = 5
2x - 3y = 7
(2, -1)
Three times the sum of two numbers is 15. One of the numbers is 9 more than one-third of the other number. What are the two numbers?
8 and -3