Download A2 Notes 2.4 More About Linear Equations

2.4
More About Linear Equations
Learning Goals
• write an equation of a line given its slope and a point on the line
MORE EQUATIONS TO KNOW
standard form: 𝐴𝑥 + 𝐵𝑦 = 𝐶
1. “A” must be positive
2. No fractions/decimals for A, B, or C
3. No common factors for A, B, or C
4. A and B cannot be 0 simultaneously
point-slope form: 𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1
EX 1
Write an equation in point-slope form of the
line with a slope of 3 and passing through −1,5
EX 2
3
Write an equation in standard form of the line 𝑦 = 𝑥 − 5
4
SLOPE RELATIONSHIPS
parallel lines
perpendicular lines
EX 3
If the slope of a line is 3, find the slopes of lines
parallel and perpendicular to the line.
EX 4
Write an equation in slope-intercept form of the line that
passes through 5, −3 and is perpendicular to 𝑦 = 4𝑥 + 1
EX 5
Write an equation in slope-intercept form of the line that
passes through −2,5 and is parallel to the x-axis.
WRITING EQUATIONS OF LINES SUMMARY
slope-intercept
form
𝑦 = 𝑚𝑥 + 𝑏
Use when given
slope and
y-intercept;
handy for graphing
and comparing
slopes
point-slope form
𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1
Use when given a
point and slope or
when given two
points
standard form
𝐴𝑥 + 𝐵𝑦 = 𝐶
Provides an easy
way to find both
intercepts and graph
EX 6
Write an equation in slope-intercept and standard forms of the
1
line with a slope of − and passing through 8, −1
2
EX 7
Write an equation in slope-intercept and standard forms of the
line that passes through −2 − 1
and 8, −3