SME
Grade 10 Math · Problem type
A parallel line through a point
Use this for “Write the equation of the line parallel to y = 3x − 4 through (2, 7).”
Chart
Given: y = 3x − 4
Parallel: y = 3x + 1
The arrows mark them parallel: both slopes are 3
(2, 7) is on Parallel: 3 × 2 + 1 = 7
This is an example. Type your own values to start a new problem.
y
=
m
x
+
b
b₁
Given line’s intercept
example
x₀
Point, x
example
y₀
Point, y
example
Formulas
b
=
y₀
−
m
×
x₀
1 = 7 − 3 × 2
Assumptions
•
Parallel lines have the same slope and different intercepts.
•
Put the point into y = mx + b to find the new intercept: b = y₀ − m × x₀.
Step-by-step
WE KNOW
m = 3, b₁ = −4, x₀ = 2, y₀ = 7
FIND
new line’s intercept (b)
Step 1 · Find new line’s intercept (b)
Use b = y₀ − m × x₀
The
point
is
on
the
new
line,
so
y₀
=
m
×
x₀
+
b
.
b
=
7
−
3
×
2
b
=
7
−
6
b
=
1
Check
Put the numbers back in. Both sides should match.
1 = 7 − 3 × 2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Parallel and perpendicular lines: transversals and proofs
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