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• Most of the equations we deal with from now on are LINEAR equations
• All linear equations (except vertical lines) have a slope.
• When asked to graph… solve the equation for y, and then use the slope, and the y-intercept
• OR…you can plug in a number for x (independent) and get a number for y (dependent) and then you have (x, y) to put on your graph.
Definition of Slope
Definition of SlopeThe slope of the line through the distinct points (x1, y1) and (x2, y2) is
where x2 – x1 = 0.
Change in yChange in x
=Rise
Run=y2 – y1x2 – x1 (x1,
y1)x1
y1
x2
y2
(x2, y2)
Risey2 – y1
Runx2 – x1
x
y
Positive Slope
x
y
m > 0
Line rises from left to right.
Zero Slope
x
y
m = 0
Line is horizontal.
m is undefined
Undefined Slope
x
y
Line is vertical.
Negative Slope
x
y
m < 0
Line falls from left to right.
Equation of a Vertical Line
A vertical line is given by an equation of the form
x = a EX:
where a is the x-intercept.
Equation of a Horizontal Line
A horizontal line is given by an equation of the form
y = b, EX:
where b is the y-intercept.
• Perpendicular Slopes are Opposite (one positive and one negative) and Reciprocals (flips of each other)