Algebra 1
Guided Notes and Practice
3.1-3.4
3.1 Solving Open Sentences in Two Variables
Solve. The domain of x is {1, 0, -2}
1.
3𝑥 + 2𝑦 = 8
2.
−3𝑥 + 2𝑦 = 8
Complete.
3.
2𝑥 + 3𝑦 = 12
(0 , _____), (_____ , 0), (4 , _____)
4.
1
3
𝑥 − 2𝑦 = 6
(_____ , 0), ( 6 , _____), (0 , _____)
Find k, so that the ordered pair satisfies the equation.
5.
𝑥 + 2𝑦 = 𝑘; (2, 1)
6.
𝑘𝑥 + 3𝑦 = 12; (3, −3)
Problem Solving:
A certain quadrilateral has three sides of equal length and its perimeter is 19 cm. Find all
integral possibilities for the lengths of the sides in centimeters. (Hint: The sum of the
lengths of any three sides of a quadrilateral must exceed the length of the fourth side.)
Luis has 95 cents in dimes and quarters. Find all possibilities for the number of each type of
coin he could have.
3-2 Graphs of Linear Equations in Two Variables
Graph each equation.
1.
𝑦−𝑥 =3
3.
𝑥 + 3𝑦 = 9
4.
Find the value of k so that point P lies on the line L.
𝑃(2,3), 𝐿: 𝑘𝑥 − 2𝑦 + 𝑘 = 0
2.
2𝑥 + 𝑦 = 5
3-3 The Slope of a Line
Slope of a line =
The slope of the line
𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
=
𝐴𝑥 + 𝐵𝑦 = 𝐶
𝑦2 −𝑦1
𝑥2 −𝑥1
(𝑥2 ≠ 𝑥1 )
(𝐵 ≠ 0) is −
𝐴
𝐵
standard form
Point Slope:
There is one and only one line L through P having slope m. An equation of L is
𝒚 − 𝒚𝟏 = 𝒎(𝒙 − 𝒙𝟏 )
Guided Examples:
1.
A ramp to provide handicapped people access to a certain building is to be
constructed with a slope of 5%. If the entrance to the building is 3 ft above ground
level, how long should the base of the ramp be?
On Your OWN
2.
A jetliner covered a horizontal distance of 5 mi while following a flight path with
slope of 2.5. How much altitude did it gain?
3-4 Finding an Equation of a Line
Review:
Slope-Intercept Form:
𝑦 = 𝑚𝑥 + 𝑏
Two lines are parallel if and only if ____________________________________.
Two lines are perpendicular if and only if ____________________________.
Guided Example:
1.
a.)
Give the standard form of the equation for the line through (5, 1), slope 2.
b.)
through (-1, 3), no slope
c.)
through (5, -2), slope
d.)
slope -3, y-intercept 7
e.)
through (1, 3) and (3, 7)
f.)
through (4, 2) and (8, 2)
1
3
2
2.
3.
Give the standard form of the equation of the line through point P that is:
a.)
perpendicular to L. P (1, 2); L: 𝑥 + 𝑦 = 4
b.)
parallel to L. P (-3, 2); L: 𝑥 − 4 = 0
Find the equations in standard form of the lines through P(-1, 2) that are
(a) parallel to, and (b) perpendicular to, L: 𝑥 − 3𝑦 = −2.