Straight-line equations are those that are first
degree in both x and y.
Slope: the measure of “steepness”
of a line. Two points on the line are needed to determine the
slope.
where (x1, y1) and (x2,
y2) are the coordinates of any two points on the line
Line Equations:
Point-Slope Form:
y - y1 = m(x - x1)
where (x1, y1) is the point and m
is the slope
Need a point and the slope to use this
form
Slope-Intercept Form:
y = mx + b where m is the slope and b is
the y-intercept (0,b)
Need a slope and a point on the line, OR
Need the slope and y-intercept
* Equations must be in the slope-intercept form (solved for y
) in order to easily “see” what the slope and y
-intercept are.
Parallel Lines… have the same slopes and
different y-intercepts
Perpendicular Lines… have slopes that
are negative reciprocals. If the slope of one line is 4 , then
the slope of the perpendicular line is .
Graphing Linear Equations:
Find the x -intercept by letting y = 0, then find the y
-intercept by letting x = 0. Plot these two points, and
draw the line that connects the two points.
If the equation is given in slope-intercept form: Plot
the y -intercept first. From the y -intercept, use the
slope information to go up/down, then right, to obtain
another point. Connect these two points, and you have
graphed the line.
Vertical Lines… are missing the y
variable. The slope of a vertical line is undefined. x = 3 is the
equation of a vertical line, where the x coordinate is always 3,
and the y coordinate can be any value.
Horizontal Lines… are missing the x
variable. The slope of a horizontal line is zero. y = 2 is the
equation of a horizontal line, where the y coordinate is always
2, and the x coordinate can be any value.
Horizontal and Vertical lines are perpendicular.
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