Solving Linear Equations in Context
A streaming service charges a $12 fee plus $4 per movie. A customer spent $44.
What is the number of movies?
What is 8 movies?
A line increases 6 units for every 2 units right and passes through (0, −3).
What is the equation?
What is y = 3x − 3?
A graph crosses the y-axis at −6 and increases.
What are the key features?
What is y-intercept −6 and positive slope?
A model: y = 8x + 50
What do slope and intercept represent?
What is $8 per hour and $50 starting value?
Solve: x − 5 ≤ 12
What is the solution?
What is x ≤ 17?
A student models a situation with 5x-3=2x+12 and finds x=5 .
What does this solution represent?
What is the value that makes both sides equal?
A table shows a constant rate but no (0, y) value.
How do you find the equation?
What is find slope then use a point to solve for the intercept?
A table: (1,3), (2,5), (3,7)
What is the equation?
What is y = 2x + 1 ?
A function models number of tickets but includes decimals.
What constraint applies?
What is x must be whole numbers and ≥ 0?
Solve: −3x > 9
What is the correct solution?
What is x < −3 ?
Two equations represent the same situation: 3x + 15 = 45 and 15 + 3x = 45.
Why are they equivalent and what is the solution?
What is x = 10 and they are equivalent by the commutative property?
A line is parallel to y = −4x + 7 and passes through (−2, 5).
What is the equation?
What is y = −4x − 3?
A graph has slope 0 and passes through y = 4 .
What does this mean?
What is a constant function?
A temperature model stops at 0.
Why?
What is values below 0 are not valid in context?
Solve: 2 < x + 1 ≤ 6
What is the solution set?
What is 1 < x ≤ 5 ?
A solution to a real-world equation is x = −2 where x represents items purchased.
Why is this solution rejected?
What is a negative number of items is not realistic?
A line is perpendicular to y = 3x − 2 and passes through (4, −1).
What is the equation?
What is y = −1/3x + 1/3? ?
A function has slope −2 and intercept 8.
What does this represent?
What is decreasing rate with starting value 8?
A model produces negative costs.
Why is this invalid?
What is cost cannot be negative?
Graph: y ≥ −x + 2
What does the graph show?
What is solid line with shading above?
Solve and verify:4(x − 3) + 2 = 3x + 10
What is the solution and how is it verified?
What is x = 4 and substitution confirms both sides are equal?
Two equations: y = 2x + 10 and 2x − y = −10
How are they related?
What is they represent the same line in different forms?
Two graphs have equal slopes but different intercepts.
What does this mean?
What is they are parallel lines?
Two pricing plans are graphed.
How do you determine the better plan?
What is compare intersection and analyze cost before/after?
A system of inequalities creates a shaded region.
What does it represent?
What is all feasible solutions?