calculating slope of a line what you should have remembered from gr. 9! see…your teachers told you...
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Calculating Slope of a Line
What you should have remembered from Gr. 9!
See…your teachers told you you’d see it again…..and???
They were correct!!
The slope of a line describes the following:• The steepness of a line• The vertical change relative to the
horizontal change• The change in the y-direction relative to
the change in the x-direction
x
y
Horizontal change (run)
(∆x)
Vertical change (rise)
(∆y)
• The slope of a linear equation (straight line) is the same everywhere.
• A line with positive slope rises from left to right.
• A line with negative slope falls from left to right.
x
y
Input: x Output: y = x + 1 (x, y)
0 1 (0, 1)
1 2 (1, 2)
2 3 (2, 3)
3 4 (3, 4)
Use points (0,1) and (2,3) to calculate the slope.
102
13slope
2
1 3
slope = ∆y ∆x
= y2 – y1
x2 – x1
• Very steep lines have large slopes, while relatively flat lines have small slopes.
More facts:
x
y
Question: Which of the three lines above have the largest slope?
Answer: The blue line!
Line of Best Fit• When calculating slope of a data set, your
data may not be perfectly linear.• You must draw a line of best fit!• Draw a line through the data points.
Line of Best Fit• Your line should pass through as many points as
possible and follow the general trend of the coordinates.
• To calculate slope, pick two coordinates that are far apart and touching/close to your line of best fit.
Slope= ∆y∆x
= y2 – y1
x2 – x1
= 2.4 – 6.88.4 – 2.0
= -4.4 6.4 = -.6875 = -.69
(x1, y1)
(x2, y2)
• Animation (regression)
• The slope of a line can be calculated from :
a table
a graph
two coordinate points on the line
using the formula :
.12
12
xx
yyslope
) y,(x and ),( 2211 yx
1
2
3
run
riseSlope