SME
Grade 9 Math · Algebra 1
Writing linear functions: slope-intercept, point-slope, standard form, parallel and perpendicular lines
Use this for “Write the equation of the line with slope 3 through (2, 5)” in point-slope and slope-intercept form.
Chart
y-intercept (0, −1)
f(2) = 5
This is an example. Type your own values to start a new problem.
y
−
y₁
=
m
(x
−
x₁
)
y
=
m
x
+
(
b
)
Formulas
b
=
y₁
−
m
×
x₁
−1 = 5 − 3 × 2
Assumptions
•
Point-slope form needs one point (x₁, y₁) and the slope m.
•
Distribute m and add y₁ to both sides to reach y = mx + b.
•
A negative x₁ reads x + 3, not x − (−3).
Step-by-step
WE KNOW
m = 3, x₁ = 2, y₁ = 5
FIND
y-intercept (b)
Step 1 · Find y-intercept (b)
Use b = y₁ − m × x₁
Distribute:
y
−
y₁
=
mx
−
mx₁,
then
add
y₁
to
both
sides;
the
number
left
is
b
.
b
=
5
−
3
×
2
y − 5 = 3(x − 2)
y − 5 = 3x − 6
y = 3x − 1
b
=
−1
Check
Put the numbers back in. Both sides should match.
−1 = 5 − 3 × 2 ✓
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Transform a function: g(x) = a·f(x − h) + k
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Parallel and perpendicular lines
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.