Download Geometry Notes Name__________________ 3.5 Write and Graph

Geometry Notes
Name__________________
3.5 Write and Graph Equations of Lines
Slope and Linear Equations Recap
Given points (x1, y1) and (x2, y2)
Slope:
m=
y2 − y1
x2 − x1
Parallel Lines
•
•
have the ______ slope
different y-intercepts
Vertical Lines
Horizontal Lines
#
0
•
have _________ slopes,
•
have equations like __________
m=
Perpendicular Lines
•
have ______________ slopes,
like 2 and _______________
0
#
•
have a slope of _____,
•
have equations like _________
m=
Slope-Intercept Form: y = mx + b
•
•
m is __________________
b is __________________
•
is_______________
(x , y )
WRITING A LINEAR EQUATION IN SLOPE-INTERCEPT FORM: y = mx + b
1.
2.
3.
4.
Determine the slope.
Plug the slope in for m and one ordered pair in for x and y in the equation.
Solve the equation for b (y-intercept)
Rewrite the equation in slope intercept form with only the slope and y-intercept filled in.
Practice: Write each of the following described equations in slope-intercept form:
1. slope of -3 and a
2. Vertical through (2, -8)
3. Horizontal through (-3, 2)
5. undefined slope
1
6. Parallel to y = ! x + 6 and
2
y-intercept of (0,-7)
4. m = !
3
4
, through (8, -4)
through (-5,2)
through (-2,0)
Write the slope-intercept equation of the line described:
7. Through P and parallel to line AB:
1
( )
9.
m =
11.
passes through (-3, 2) and (-2, -1)
5
passes thru
0,5
13. through (-2, 1) and (-5, 1)
15.
passes thru
( −6, 0 )
perpendicular to
3
y = x − 15
2
8. Through P and perpendicular to line AB:
10.For the line graphed:
12.
passes thru
(2, !3)
and
(2,5)
14. Perpendicular to x= -2; through (-4,5)
16.
passes thru
parallel to
(!6, 0)
3x ! 2y = 30