Mixed Questions
What type of graph shows descriptions or categories instead of exact numbers?
What is Qualitative graph?
Table: x: 1, 2, 3 → y: 4, 5, 6. Is this a function?
Yes — every x has exactly one y.
Table: x: 1,2,3,4 → y: 3,4,5,6. What is the rule?
y = x + 2
What does slope measure?
The steepness /
rate of change of a line /
/ rise over run.
In y = mx + b, what does m represent?
What type of graph uses numerical data that can be measured?
What is Quantitative graph
Mapping: 1→2, 1→3, 2→4. Is this a function? Why or why not?
No — the input 1 maps to two different outputs (2 and 3).
Table: x: 1,2,3,4 → y: 2,4,6,8. What is the rule?
y = 2x
Find the slope between (1, 2) and (3, 8).
slope = (8-2)/(3-1) = 6/2 = 3
In y = mx + b, what does b represent?
What is the y-intercept?
Solve the equation:
154 = -4(8 + 6r) + 24r
What type of solutions does it have?
No Solution
A graph passes through the points
(0,−2), (2,4), and (4,10).
What is the equation?
y=3x−2
Table: x: 0,1,2,3 → y: 1,3,5,7. What is the rule?
y = 2x + 1
What is the slope of a horizontal line?
0
Write the equation of a line with slope 4 and y-intercept -3.
What is y=4x-3
A graph shows the temperature every hour from 8 A.M. to 5 P.M. Is it qualitative or quantitative?
Quantitative
A vending machine charges $2 for the first item and $1.50 for each additional item.
Write an equation relating the number of additional items x, to the total cost, y.
y=1.5x+2
If f(x) = 3x - 4, find f(5).
f(5) = 3(5) - 4 = 11
What is the slope of a vertical line?
Undefined
A line has slope 2 and passes through (1, 5). Write its equation in slope-intercept form
y = 2x + 3,
since 5 = 2(1) + b,
gives b = 3
Solve the equation:
0 = −4 p + 4p
What type of solutions does it have?
What is Infinite Solutions?
Table: x: 2, 3, 3, 5 → y: 6, 7, 8, 9.
Is this a function? Explain.
No — the input x = 3 appears twice with two different outputs (7 and 8).
Table: x: -1,0,1,2 → y: 5,2,-1,-4. What is the function rule?
y = -3x + 2
A line passes through (-2, 5) and (4, -7). Find the slope and say whether the line rises or falls left to right.
slope = (-7-5)/(4-(-2)) = -12/6 = -2,
so the line falls left to right.
Compare y = 2x + 1 and y = 2x - 5 without graphing. What type of relationship do these lines have?
They are parallel — same slope (2), different y-intercepts — so they never intersect.