Arithmetic Sequences
Is the sequence arithmetic? Explain.
6, 9, 12, 15, 18, ...
Yes, has a common difference of 3
Given x + 2y = 3, find the slope of the line
m = -1/2
Graph the line y = (2/3)x - 5
y-int on (0, -5)
slope is up 2, right 3 AND down 2, left 3
Write the equation of the line in slope-intercept form that has a slope of -2 and passes through the point (0, -3)
y = -2x - 3
Do the following points create a linear function? Explain why or why not.
{(-2, -7), (-1, 4), (0, 1), (1, -2)}
Yes; a constant change in x corresponds to a constant change in y
Is the sequence arithmetic? Explain.
6, 12, 24, 48, ...
No--no common difference; cannot multiply in an arithmetic sequence
What is the slope of a horizontal line?
Zero
State the x- and y-intercepts, then graph
2x - 4y = 12
x-int: (6, 0)
y-int: (0, -3)
Write the equation of the line that has an undefined slope and passes through the point (7, -15)
x = 7
Rewrite the equation in standard form:
y = -2/3 x + 7
2x + 3y = 21
What does a10 = 17 mean?
The 10th term in the sequence is 17
Find the slope of the line containing the points
(1, -14) and (-2, -5)
-3
Graph the line y + 2 = -1/2 (x - 3)
Line contains the point (3, -2)
slope is -1/2: Down 1, right 2 AND up 1, left 2
Write the equation of the line in slope-intercept form that passes through the point (-3, 2) and has a slope of -5/3
y = (-5/3)x - 3
A DJ charges a $250 flat fee for his services, plus $75 per hour.
A) Write a linear function that shows cost as a function of time
B) How much does it cost to have the DJ for 5 hours?
C) If you spent $475, how many hours?
A) y = 75x + 250
B) $625
C) 3 hours
4, 1, -2, -5, ...
an = 4 - 3 (n-1)
Find the slope of the line given the table:
x y
-3 -12
-1 -4
2 8
4
Graph the line y = 2
Horizontal line through (0, 2)
Write the equation of the line that passes through the points (-4, -3) and (8, -12) in point-slope form.
y + 3 = -3/4 (x + 4)
OR
y + 12 = -3/4 (x - 8)
Write the explicit formula for the sequence, and then find the 500th term:
-10, -7, -4, -1, 2, ...
an = -10 + 3 (n - 1)
a500 = 1,487
Find the 235th term in the sequence:
-12, -5, 2, 9, ...
a235 = 1626
A computer virus protection scanner is scanning files on a computer. It scanned a total of 420 files after 16 seconds and it scanned a total of 650 files after 26 seconds. Find and interpret the rate of change.
The virus protection scanner can scan 23 files per second
Rewrite the equation in slope-intercept form, then graph: 4x + 3y = 15
y = (-4/3)x + 5
Write the equation of the line that passes through the points (-9, -1) and (-3, 1). Your final answer should be in standard form.
y = (1/3)x + 2
x - 3y = -6
A school is making t-shirts with its logo on them. It costs $190 to make 20 t-shirts and it costs $430 to make 50 t-shirts.
A) Write an equation that shows how much it costs to make the t-shirts
B) Interpret the slope and y-int of the problem
A) y = 8x + 30
B) Slope: it costs $8 per shirt
y-int: The company charges a $30 flat fee