STRAND: Algebra
TOPIC:
Coordinates & graphs
Measuring the rise and
the run
To measure the rise and the run for a straight line, follow these steps:
1. Select two points on the line. If the line goes through the origin, it is best to select the origin and any other point. If the line
cuts both axes, select the x-intercept and the y-intercept.
2. Construct the gradient triangle, so that the two points are the vertices.
3. Measure the horizontal distance (that is, the distance along the horizontal side of a triangle) between the two points. This
distance represents the run. Note that the run is always positive.
4. Measure the vertical distance (that is, the distance along the vertical side of a triangle) between the two points. This distance
represents the rise. Note that if the line slopes upward from left to right, the rise is positive, while if the line slopes
downward, the rise is negative.
WORKED Example
State the rise and the run for each of the following straight lines.
y
a
b
y
4
3
2
1
–4 –3 –2 –1
–1
–2
–3
–4
4
3
2
1
1 2 3 4 x
–3 –2 –1–1
–2
–3
–4
1 2 3 4 5 6
THINK
WRITE/DRAW
a
a
1
Since the line goes through the origin,
select the origin and some other point.
Draw the gradient triangle so that the
selected points are the vertices.
y
4
3
2
1
–4 –3 –2 –1
–1
–2
–3
–4
2
3
Measure the distance along the horizontal
side of the triangle (that is, how much it is
from 0 to 2). Hence state the value of the
run.
Measure the distance along the vertical
side of the triangle (that is, how much it is
from 0 to 3) to find the value of the rise.
Since the line slopes upward from left to
right, the rise is positive.
x
3
2
1 2 3 4
Run = 2
Rise = 3
 John Wiley & Sons Australia, Ltd 2001
STRAND: Algebra
TOPIC:
Coordinates & graphs
SKILLBUILDER: Measuring the rise and
the run
THINK
WRITE/DRAW
b
b
Since the line cuts both axes, select the
x- and y-intercepts. Draw the gradient
triangle so that the selected points are the
vertices.
1
y
4
3
2
1 –2
–3 –2 –1–1
–2
–3
–4
3
x
Run = 6
Measure the distance along the horizontal
side of the triangle (it is from 0 to 6) and
hence state the value of the run.
Measure the distance along the vertical
side of the triangle (that is, from 0 to 2) to
find the value of the rise. Since the line
slopes downward from left to right, the rise
is negative.
2
6
1 2 3 4 5 6
Rise = −2
Try these
State the rise and the run for each of the following straight lines.
1
2
y
4
4
3
2
1
3
2
1
–3 –2 –1
–1
–2
–3
3
5
1 2 3 4 5 6
x
1 2 3 4 5 6
x
1 2 3 4 5 6
x
1 2 3 4 5 6
x
y
4
3
2
1
1 2 3 4 5 6
x
–3 –2 –1–1
–2
–3
6
y
4
3
2
1
–3 –2 –1
–1
–2
–3
–3 –2 –1–1
–2
–3
4
y
5
4
3
2
1
–3 –2 –1
–1
–2
–3
y
y
4
3
2
1
1 2 3 4 5 6
x
–3 –2 –1–1
–2
–3
 John Wiley & Sons Australia, Ltd 2001
STRAND: Algebra
TOPIC:
Coordinates & graphs
7
SKILLBUILDER: Measuring the rise and
the run
8
y
4
3
2
1
4
3
2
1
–3 –2 –1
–1
–2
–3
9
1 2 3 4 5 6
x
–3 –2 –1
–1
–2
–3
10
y
1 2 3 4 5 6
x
y
3
2
1
4
3
2
1
–3 –2 –1–1
–2
–3
y
1 2 3
x
–4 –3 –2 –1–1
–2
–3
–4
1 2
x
 John Wiley & Sons Australia, Ltd 2001