UNIT 2 – ANALYTIC GEOMETRY
LESSON 1 – GET READY
EQUATION OF A LINE
𝒚 = 𝒎𝒙 + 𝒃
SLOPE
𝒎=
𝒓𝒊𝒔𝒆
𝒓𝒖𝒏
or
𝒚 −𝒚
𝒎 = 𝒙𝟐 −𝒙𝟏
𝟐
Slope
𝟐
Example ① Calculate each slope.
a) 𝐴(1, −2); 𝐵(−2, 3)
b) 𝐶(1, −1); 𝐷(1, 3)
y-intercept
𝑦
c)
𝑥
3
Example ② Determine the equation of the line that has slope of − 4 and y-intercept of 2.
Example ③ Determine the equation of the line that passes through 𝐴(2, 3) and 𝐵(−2, 4).
PARALLEL AND PERPENDICULAR LINES
Parallel lines have equal slopes.
1
1
Ex: 𝑦 = 2 𝑥 − 5 and 𝑦 = 2 𝑥 + 3
Perpendicular lines have negative
reciprocal slopes.
3
2
Ex: 𝑦 = 2 𝑥 − 5 and 𝑦 = − 3 𝑥 + 3
Example ④ Given the line 𝑦 = −2𝑥 + 1, state:
a) the slope of a line parallel to the given line _____________________
b) the slope of a line perpendicular to the given line ________________
c) the slope of a horizontal line ________________________________
d) the slope of a vertical line __________________________________
Example ⑤ Find an equation for the line that
a) is parallel to the line defined by 𝑦 = 4𝑥 − 1 and passes through 𝐴(0,4)
4
b) is perpendicular to the line defined by 𝑦 = − 3 𝑥 + 2 and passes through 𝐵(4,1).