Coordinates & Linear
Equations
Coordinates
Coordinates – A group of numbers
used to indicate the position of a point,
line or plane
Horizontal – Parallel to the plane of
the horizon; at a right angle to the
vertical
Vertical – An upright line where the
top is directly above the bottom
Plot – Mark a position on a chart or
graph
(2 , 6)
2 Represents the point on the x-axis
6 Represents the point on the y-axis
Let's plot the values!
Let's look at the
graph paper
Let's Practice!
Plotting
Plott the following on the
graph
(-4,1)
(2,-5)
(-5,-4)
(1,-6)
Plotting
Plott the following on the
graph
(-4,1)
(2,-5)
(-5,-4)
(1,-6)
Plotting
Plott the following on the
graph
(-4,1)
(2,-5)
(-5,-4)
(1,-6)
Plotting
Plott the following on the
graph
(-4,1)
(2,-5)
(-5,-4)
(1,-6)
Plotting
Plott the following on the
graph
(-4,1)
(2,-5)
(-5,-4)
(1,-6)
Interpritaion
Plott the following on the
graph
Interpritaion
Plott the following on the
graph
(5,5)
Interpritaion
Plott the following on the
graph
(5,5)
(-6,3)
Interpritaion
Plott the following on the
graph
(5,5)
(-6,3)
(1,-4)
(1,-6)
Interpritaion
Plott the following on the
graph
(5,5)
(-6,3)
(1,-4)
(3,1)
MORE
Interpritaion
Plott the following on the
graph
MORE
Interpritaion
Plott the following on the
graph
(2,2)
(-5,1)
(-2,-4)
(-5,-2)
Linear Relationship
A linear relationship is characterized by
an increase or decrease of one variable
as the other one also changes.
When the variables are plotted in a
graph, a straight line is formed.
Let's plot the values!
Deformation (mm)
8
6
4
The variables form
a straight line!
2
0
0
1
2
3
Force (N)
4
5
6
Slope-intercept Form
The equation of the line
can be written using the
slope-intercept form.
y = mx + b
slope
y-intercept
Slope describes the steepness
and the direction of a line.
It is calculated using:
How do you calculate
the slope of a line?
m=
rise
run
=
Δy
Δx
=
y2 - y 1
x2 - x1
(3,-6) and (4,-2)
It is calculated using:
Let's try some examples for
solving for the gradient
m=
rise
run
=
Δy
Δx
=
y2 - y 1
x2 - x1
Let's calculate the slope!
Deformation (mm)
12
10
8
rise
run
y2 - y 1
m=
x2 - x 1
x2 , y 2
6
m=
x1 , y 1
rise
4
run
2
m=
0
0
1
2
3
Force (N)
4
5
6
m= 4
-2 - (-6)
4-3
Let's try some more
examples for solving for the
gradient
(-2,0) and (8,3)
(-2.5 ,2) and (3.5 , -1)
m=
rise
run
=
Δy
Δx
=
y - y1
2
x2 - x 1
(10, 6) and (4,-2)
(-3,-2) and (-6,5)
How do you calculate the
y-intercept of a line?
Y-intercept is the point where
the graph crosses the y-axis.
Calculate the y-intercept by
determining the value of y
when x is zero.
Let's calculate the slope!
Deformation (mm)
12
10
8
rise
run
y2 - y 1
m=
x2 - x 1
x2 , y 2
6
m=
x1 , y 1
rise
4
run
2
m=
0
0
1
2
3
Force (N)
4
5
6
m= 4
-2 - (-6)
4-3
Let's calculate the y-intercept!
Substitute the values
of m = 4 and one
data point (3,-6) in
the equation. Then,
solve for b.
y = mx + b
-6 = 4 (3) + b
b = 12 + 6 = 18
please note that you can use any data point on the straight line ( (3, -6)
or (4, -2)) the answer WILL ALWAYS BE THE SAME
m = 4 was solved for in previous steps
Let's calculate the y-intercept!
Deformation (mm)
12
10
8
6
4
2
y - intercept, b = 18
0
0
1
2
3
Force (N)
4
5
6
Equation of the Line
As the force increases,
the deformation also
increases.
12
Deformation (mm)
The two variables have
a linear relationship.
10
8
6
4
The equation of the line is
y = 4x + 18.
2
0
0
1
2
3
Force (N)
4
5
6
Let's Practice!
Example 1
Y vs X
12
10
Find the following based
on the graph.
8
6
Y
slope of the line
4
y-intercept
2
equation of the line
0
-3
-2
-1
0
1
X
2
3
4
5
Answers
Y vs X
12
10
Find the following based
on the graph.
8
6
Y
slope of the line 2
4
y-intercept
2
equation of the line
0
-3
-2
-1
0
1
X
2
3
4
5
Answers
Y vs X
12
10
Find the following based
on the graph.
8
6
Y
slope of the line 2
4
y-intercept
2
4
equation of the line
0
-3
-2
-1
0
1
X
2
3
4
5
Answers
Y vs X
12
10
Find the following based
on the graph.
8
6
Y
slope of the line 2
4
y-intercept
2
4
equation of the line
0
-3
y=2x + 4
-2
-1
0
1
X
2
3
4
5
Example 2
Y vs X
12
10
Find the following based
on the graph.
8
6
Y
slope of the line
4
y-intercept
2
equation of the line
0
-15
-12
-9
-6
-3
X
0
3
6
9
Answers
Y vs X
12
10
Find the following based
on the graph.
1
slope of the line =
3
8
6
Y
4
y-intercept = -1
2
equation of the line
1
y=
-1
3
0
-15
-12
-9
-6
-3
X
0
3
6
9
Example 3
Y vs X
12
10
Find the following based
on the graph.
(-1, 8.5)
8
6
Y
slope of the line
4
y-intercept
2
equation of the line
0
-3
-2
-1
(2, 4)
0
1
X
2
3
4
5
Answers
Y vs X
12
10
Find the following based
on the graph.
(-1, 8.5)
8
6
Y
slope of the line -1.5
4
y-intercept
2
equation of the line
0
-3
-2
-1
(2, 4)
0
1
X
2
3
4
5
Answers
Y vs X
12
10
Find the following based
on the graph.
(-1, 8.5)
8
6
Y
slope of the line -1.5
4
y-intercept 1
2
equation of the line
0
-3
-2
-1
(2, 4)
0
1
X
2
3
4
5
Answers
Y vs X
12
10
Find the following based
on the graph.
(-1, 8.5)
8
6
Y
slope of the line -1.5
4
y-intercept 1
2
equation of the line
0
-3
y = -1.5x + 1
-2
-1
(2, 4)
0
1
X
2
3
4
5
Thank you for listening!
For our next topic, read about quadratic functions.
References:
CK-12. Linear Relationships. Last Accessed October 20, 2021 from https://www.ck12.org/book/ck-12-probability-and-statistics-concepts/section/11.1/.
CK-12. Determining the Equation of a Line. Last Accessed October 19, 2021 from https://www.ck12.org/algebra/determining-the-equation-of-a-line/.