Page 6
Representations of Functions
The 4 Types of Slope
Slope from a Graph
slope_graphs_2points_equations.pdf |
slope_to_line.pdf |
Slope from 2 Points
slope_twopoints.pdf |
Slope from a Table
This video is great because it builds up difficulty levels...it goes from a consistent x-axis to an inconsistent x-axis. She also mentions 2 'weird' cases because we know, when 0 is involved, THINGS GET WEIRD.
slope_tables.pdf |
Slope from an Equation
If y is isolated or alone, then m (slope) is the number attached to the x.
(1) y = 2x +3
(2) y = -8x + 4
(3) y = x + 9
(4) y = 3/4 x + 1/4
ANSWERS:
(1) m = 2
(2) m = -8
(3) m = 1
(4) m = 3/4
_______________________________
If y has a coefficient (a number attached to y), you must divide by that number.
(5) 2y = 18x + 7
(6) 9y = 54x + 4
(7) 3y = 8x - 10
(8) 10y = -4x + 24
(9) 5y = 5x - 5
(10) -4y = -2x + 16
ANSWERS:
(5) m = 18/2 = 9
(6) m = 54/9 = 6
(7) m = 8/3 (cannot be simplified)
(8) m = -4/10 = -2/5 (don't lose your negative!)
(9) m = y = 5/5 = 1
(10) m = -2/-4 = 1/2 (negative divided by negative equals positive)
(1) y = 2x +3
(2) y = -8x + 4
(3) y = x + 9
(4) y = 3/4 x + 1/4
ANSWERS:
(1) m = 2
(2) m = -8
(3) m = 1
(4) m = 3/4
_______________________________
If y has a coefficient (a number attached to y), you must divide by that number.
(5) 2y = 18x + 7
(6) 9y = 54x + 4
(7) 3y = 8x - 10
(8) 10y = -4x + 24
(9) 5y = 5x - 5
(10) -4y = -2x + 16
ANSWERS:
(5) m = 18/2 = 9
(6) m = 54/9 = 6
(7) m = 8/3 (cannot be simplified)
(8) m = -4/10 = -2/5 (don't lose your negative!)
(9) m = y = 5/5 = 1
(10) m = -2/-4 = 1/2 (negative divided by negative equals positive)
Slope from Similar Triangles
• In the image below, the slope of the line connecting Q to R is m = rise/run = 1/2
The line connecting R to S has a slope of m = rise/run = 3/6 which reduces to 1/2
We can also see that the line connecting Q to S has a slope of m = 4/8 = 1/2
• Thus, starting from Point Q, we can create a line with a slope of any equivalent fraction to 1/2
(ex: We can rise 2, run 4...we can rise 10, run 20... we can rise -5 (down), run -10 (left)...)
The line connecting R to S has a slope of m = rise/run = 3/6 which reduces to 1/2
We can also see that the line connecting Q to S has a slope of m = 4/8 = 1/2
• Thus, starting from Point Q, we can create a line with a slope of any equivalent fraction to 1/2
(ex: We can rise 2, run 4...we can rise 10, run 20... we can rise -5 (down), run -10 (left)...)
• In the image below, the slope from A to C is m = rise/run = 4/6 = 2/3
The slope from C to E is m = rise/run = 2/3
• Because of these equivalent slopes, we can say that ∆ABC and ∆CDE are similar triangles.
(Essentially, ∆ABC is a "scaled up" version of ∆CDE.)
• We could start from Point A and rise 2, run 3 and end up back on the line.
From Point A, we could rise 6, run 9 and end up back on the line. (We would actually end up at Point E.)
The slope from C to E is m = rise/run = 2/3
• Because of these equivalent slopes, we can say that ∆ABC and ∆CDE are similar triangles.
(Essentially, ∆ABC is a "scaled up" version of ∆CDE.)
• We could start from Point A and rise 2, run 3 and end up back on the line.
From Point A, we could rise 6, run 9 and end up back on the line. (We would actually end up at Point E.)