SME
Grade 8 Math · Functions
Linear functions (y = mx + b)
Use this for “For y = 2x + 1, what is y when x = 3?” and the line’s slope and intercept.
Chart
y = 2x + 1
Slope m = 2: up 2 for every 1 across
Intercept b = 1: it crosses the y-axis at (0, 1)
y = 2 × 3 + 1 = 7 when x = 3
This is an example. Type your own values to start a new problem.
y
=
m
x
+
b
x
Input x
example
y
Output y
calculated
Formulas
y
=
m
×
x
+
b
(output
y
=
slope
×
input
x
+
y-intercept)
7 = 2 × 3 + 1
Assumptions
•
The graph is a straight line, so y changes at a constant rate.
•
m is the slope: the change in y for every 1 more x.
•
b is the y-intercept: y when x = 0.
•
A negative m makes the line fall to the right.
Step-by-step
WE KNOW
x = 3 (input x), m = 2 (slope), b = 1 (y-intercept)
FIND
output y (y)
Step 1 · Find output y (y)
Use y = m × x + b (output y = slope × input x + y-intercept)
Start
at
b
,
then
add
the
slope
once
for
every
step
of
x
.
y
=
2
×
3
+
1
y
=
6
+
1
y
=
7
Check
Put the numbers back in. Both sides should match.
7 = 2 × 3 + 1 ✓
Topic check
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