Graphing Linear Equations
|Graphing Equations Using Two Points
||Use the equation to find the coordinates of any two
points on the line. Draw the line representing the equation by
connecting them. The two points chosen can be the x- and y-intercepts.
|Graphing Equations Using a Point and the Slope
||Graph one point and use the slope to find another point
by moving the distance of the change in y and then the distance of the
change in x from that point. When the equation is in point-slope form, y
= m( x - x1), use the point ( x1, y1)
and the slope m. When the equation is in slope-intercept form, y = mx +
b, use the point (0, b) and the slope m.
Graph -2x + 3y = 9 by using the slope and y -intercept.
|3y = 2x + 9
||Solve the equation for y.
||(0, 3) is on the line.
|slope of line:
||Move up 2 units, then right 3 units from that point.
Parallel and Perpendicular Lines
||Lines in the same plane that never intersect are called
parallel lines. If two nonvertical lines have the same slope, then they
are parallel. All vertical lines are parallel.
||Lines that intersect at right angles are called
perpendicular lines. If the product of the slopes of two lines is -1,
then the lines are perpendicular. The slopes of two perpendicular lines
are negative reciprocals of each other. In a plane, vertical lines and
horizontal lines are perpendicular.
Determine whether the graphs of 2 y = -3 x + 4 and 3 y = 2 x - 9 are
parallel, perpendicular, or neither.
Rewrite each line in slope-intercept form to identify its slope.
|2 y = -3 x +
||3 y = 2 x - 9
Since , these lines are perpendicular.
Midpoint of a Line Segment
|Midpoint of a Line Segment
||The midpoint of a line segment is the point that is
halfway between the endpoints of the segment. The coordinates of the
midpoint of a line segment whose endpoints are at ( x1, y1)
and ( x2, y2) are given by
The midpoint of a segment is M (2, 3) and one endpoint is B ( -1, 5). Find
the coordinates of the other endpoint.
Let M(2, 3) = (x, y) and B( -1, 5) = ( x1, y1).
Form two equations by setting the x-coordinates equal to each other and the
y-coordinates equal to each other.
Coordinates of the other endpoint: (5, 1).