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3.2 Slope of a line
To find the slope of a line when you know the coordinates of two of the points on the line use
coordinates of two of the points on the line, use y − y2
the formula where (x
m= 2
1,y1) and
x2 − x2
(x2,y2) are two points on the line.
Find the slope of the line that passes through the points (‐4,3) and (‐3,‐4) 1
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Find the slope of the line that passes through the points (‐3,‐3) and (5,6).
Find the slope of the line that passes through the points (‐6,3) and (2,3).
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Find the slope from the graph.
(‐5,2)
• (0,5)
(0 5)
•
•
•
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A line has a positive slope if the line rises to the right
g
p
A line has a negative slope if the line falls to the right.
A line has a slope of 0 if the line is horizontal.
A line has an undefined slope if it is vertical.
You can write the equation of a line in slope‐intercept form, y = mx + b, where m is the slope and b is the y‐intercept.
Write each of the following equations in slope‐intercept form. Then state the slope of the line and graph.
x + 3y = ‐6
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3x + 4y = 12
X – 4 = 0
y = ‐3x
y + 5 = 0
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Graph a line when you know one point and the slope.
(‐2,3) m = 5/4
(‐2,‐4); m = 4
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Lines that are parallel have the same slope.
Lines that are perpendicular have slopes that are opposite (sign) reciprocals of each other.
Determine if the pair of lines are parallel, perpendicular, or neither.
Example: Line 1 passes through (15,9) and (12,‐7)
Line 2 passes through (8, ‐4) and (5,‐20)
x + 4y = 7 and 4x – y = 3
4x – 3y = 6 and 3x – 4y = 2
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x = 6 and 6 – x = 8
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