SME
Grade 9 Math · Problem type
Parallel and perpendicular lines
Use this for “Write the line through (4, 3) perpendicular to y = 2x + 1.”
Chart
Given line: y = 2x + 1
New line: y = (−1/2)x + 5
They cross at (8/5, 4.2).
2 × 8/5 + 1 = 4.2
−1/2 × 8/5 + 5 = 4.2
This is an example. Type your own values to start a new problem.
y
=
m₁
x
+
b₁
y
=
−1
2
m₂
x
+
b₂
x₁
Point’s x
example
y₁
Point’s y
example
k
Parallel or perpendicular
example
Formulas
m₂
=
m₁
when
k
is
1,
−
1
m₁
when
it
is
2
−
1
2
=
2
when
perpendicular
is
1,
−
1
2
when
it
is
2
b₂
=
y₁
−
m₂
×
x₁
5
=
3
−
(−
1
2
)
×
4
Assumptions
•
Parallel lines have the same slope.
•
Perpendicular slopes multiply to −1: flip the slope and change its sign.
•
Then put the point into y = mx + b to find b.
Step-by-step
WE KNOW
m₁ = 2, b₁ = 1, x₁ = 4, y₁ = 3, k: perpendicular
FIND
slope of the new line (m₂), y-intercept of the new line (b₂)
Step 1 · Find slope of the new line (m₂)
Use m₂ = m₁ when k is 1, −1 ÷ m₁ when it is 2
Perpendicular: the negative reciprocal, so the two slopes multiply to −1.
m₂
=
−
1
m₁
m₂
=
−
1
2
m₂
=
−
1
2
Step 2 · Find y-intercept of the new line (b₂)
Use b₂ = y₁ − m₂ × x₁
The
new
line
passes
through
the
point:
put
it
into
y
=
m₂x
+
b₂
and
solve
for
b₂
.
b₂
=
3
−
(−
1
2
)
×
4
b₂
=
3
−
(−2)
b₂
=
5
Check
Put the numbers back in. Both sides should match.
−
1
2
=
−
1
2
✓
5
=
3
−
(−
1
2
)
×
4
✓
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Writing linear functions: slope-intercept, point-slope, standard form, parallel and perpendicular lines
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A linear model in a story
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