Linear equations describe relationships where one variable changes at a constant rate as the other changes. There are three types of linear relationships: positive, where the line increases from left to right; negative, where the line decreases; and zero, where the line is flat. Key aspects of linear equations include the slope, which measures the rate of change; the y-intercept, which is the point where the line crosses the y-axis; and the x and y axes which form the coordinate plane with four quadrants used to locate points.

1. Linear Equations
I can recognize a linear relationship
from a table, graph, and/or equation

2. Why-

3. A relationship between two quantities
in which one variable changes at a
constant amount as the other variable
changes by a constant amount.
Linear Relationship
Positive Linear
Relationship- The
line
increases(rises)
from left to right.
y=mx+b
Negative Linear
Relationship- The
line
decreases(falls)
from left to right.
y=-mx+b
Zero Linear
Relationship- The
line neither increases
or decreases from
left to right.
y=(any number)

4. x
y
k 
X (variable) Y(total)
1 2
2
1
2


k
k
kxy 

5. 110510  x
110  xy
11065 

6. bmxy 
32  xy
Slope
y-intercept

7. X Y
1 2
2 3
1
1
1
12
23



m
Slope

8. X-Axis: it’s the axis that runs
horizontal, where point (x,y)
y=0, on the coordinate plane. The
x-axis runs from left to right.
Y-Axis: it’s the axis that runs
vertical, where point (x,y) x=0,
on the coordinate plane. The y-
axis runs from top to bottom.
X-Axis
Y-Axis
x-axis
y-axis
Origin
(0,0)
Origin
(0,0)

9. The point where the graph of a
line passes the y-axis. In equation
y=mx+b, the y-intercept equals
the b value (0,b).
Y-intercept = (0,3)
Y-intercept
Y-Intercept
32  xy
X Y
-1 1
0 3
1 5
y-intercept

10. Quadrant II
(-,+)
Quadrant I
(+,+)
Quadrant III
(-,-)
Quadrant IV
(+,-)

11. Liner Relationship
positive-negative-zero
d) e) f)
a) b) c)

12. Label the following points and
quadrant.
d) e) f)
a) b) c)
Quadrant II
(-,+)