5-3, 5-4, and 5-5 Forms of Linear Equations
Quick Review
The graph of a linear e quation is a line. You can w rite a
linear equation in different forms.
The slope-intercept form of a lin ear eq u a tio n is
y = mx + b, where m is the slope an d b is the y-intercept.The point-slope form of a linear eq u a tio n is
y - jq = m(x - xx), where m is th e slope a n d (xj, y x) is a
point on the line.
The standard form of a linear eq u a tio n is Ax + By = C,
where A, B, an d C are real num bers, an d A and B are not
both zero.
Ex a m p l e
What is an equation of the line that has slope — 4 and
passes through the point ( — 1,7)?
y-yi = m(x-^ xx) Use poi nt - sl ope f or m.
v _ 7 = — 4 (x - ( - I ' D Substitute ( - 1 ,7 ) for (x,, yx) and
y -4 form.
y - 7 = — 4(x + 1) Si m p l i f y i n s i d e g r o u p i n g sy m b o l s.An equation of th e line is y - 7 = - 4 ( x + 1).
Ex e r c i se s
Write an equation in slope-intercept form of the line that
passes through the given points.- (-3,4), (1,4) 19. (3, - 2 ) , (6,1)
Graph each equation.- y = 4x - 3
- y + 3 = 2(x - 1)
23. y = 2
25. x + 4 y = 10
5-6 Parallel and Perpendicular Lines
Quick Review Ex e r c i s e s
Parallel lines are lines in th e sam e p lan e th at never Write an equation of the line that passes through the given
intersect. Two lines are perpendicular if they intersect to point and is parallel to the graph of the given equation.
form right angles. 26. (2, - l ) ; y = 5 x - 2 27. (0, —5); y = 9xEx a m p l e Determine whether the graphs of the two equations are
Are the graphs of y = |x + 5 and y = — |x + 2 parallel, parallel, perpendicular,^ or neither.^ Explain.
perpendicular, or neither? Explain. 28. y = 6x + 2 29. 2x - 5y = 0
The slope of th e graph of y = | x + 5 is f. 18x - 3y = 15 y + 3 = | x
The slope of th e graph of y = -\ x + 2 is — |.
A f O \ Write an equation of the line that passes through the
If !)" - 1 given point and is perpendicular to the graph of the
The slopes are opposite reciprocals, so th e graphs
are perpendicular.given equation.- (3, 5 );y = —3x + 7 31. (4,1 0 );y = 8 x - 1
PowerAlgebra.com | Ch ap t er 5 Ch ap t er Revi ew^355