Proportional or Not?
A recipe calls for 2 cups of sugar for every 3 cups of flour. If you double the recipe, is the relationship between sugar and flour proportional?
Yes — doubling both keeps the same ratio (2:3).
What would the point (0, 5) represent on a graph of a line showing the cost of a phone plan?
The starting cost (no data used yet) — the y-intercept.
Write an equation for a line with slope 2 and y-intercept 5.
y=2x+5
In y=50x, where y is pay and x is hours, what does 50 represent?
The hourly rate (slope).
Find the slope between (1, 2) and (3, 6).
2
You earn $36 for 4 hours of babysitting. Is your pay proportional to hours worked? What’s the unit rate?
Yes; $9/hour.
If a line on a graph passes through (0, 0) and (2, 6), what’s the slope?
(2−0) / (6−0) = 3
The equation y=4x — proportional or non-proportional and explain how you know?
Proportional (no intercept).
A gym charges $30 to join and $10 per month. Write an equation for total cost y after x months.
y=10x+30
Find the slope of the line through (2, 5) and (4, 9).
2
A taxi charges $4 per ride plus $2 per mile. Is cost proportional to miles driven?
No — there’s a fixed starting fee (not proportional).
A graph shows the relationship between distance (y) and time (x). The slope is 60. What does that mean?
The object travels 60 units (e.g., miles) per hour.
If a line passes through (0, 3) and (2, 9), write its equation.
y=3x+3
In y=−5x+40, what does the –5 mean if y is temperature and x is hours?
The temperature drops 5° each hour.
Write an equation for the line through (1, 4) and (3, 10).
Slope = 3; y=3x+1
Graph A goes through (0, 0) and (3, 6). Graph B goes through (0, 2) and (3, 8). Which graph represents a proportional relationship? And how do you know?
Graph A — it passes through the origin.
A line passes through (0, 4) and (3, 10). What is the slope, and what does it represent?
Slope = (10−4) /(3−0) = 2. The y-value increases by 2 for each x increase of 1.
Write an equation for a line with a slope of –2 that passes through (0, 6).
y=−2x+6
A tank starts with 100 gallons and leaks 4 gallons per hour. Write the equation and find how much is left after 6 hours.
y=−4x+100; after 6 hours: y=76
The line through (–2, 7) and (2, –5): find the slope and y-intercept.
Slope = −3 Equation : y=−3x+1
A store sells 5 notebooks for $12.50 and 8 notebooks for $20. Is the relationship proportional? And what is the unit rate?
Yes — $2.50 per notebook both times.
A line crosses the y-axis at 7 and rises 3 for every 2 it runs. Write its equation.
y = 3/2 x + 7
The line goes through (2, 8) and (5, 17). Write its equation.
Slope = (17−8) / (5−2) = 3, y=3x+2
You’re renting a kayak for $15 per hour plus a $10 deposit. How long until your total cost is $70?
70=15x+10⇒x=4 hours
Write the equation of the line through (–3, 4) and (2, –1).
Slope: -1 Equation : y=−x+1