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Parallel lines do not coincide.
They form NO solution.
GRAPHING PARALLEL LINES
Explanation of a system of equations that form parallel lines
Standard Form
Ax + By = C
-2x + y = 2 -2x + y = 4
FIRST STEP: CREATE INITIAL LINEAR LINES
X- & Y- INTERCEPT TECHNIQUE
Discover the X- & Y-intercept
-2x + y = 4
if x = 0, then
-2(0) + y = 4
0 + y = 4
y = 4
y -intercept = 4 (0, 4)
-2x + y = 2
if x = 0, then
-2(0) + y = 2
0 + y = 2
y = 2
y -intercept = 2 (0, 2)
Equation #1
X & Y- Intercept
Ax + By = C
-2x + y = 2
Discover the y-intercept
Equation #2
X & Y- Intercept
Ax + By = C
-2x + y = 4
Discover the y-intercept
Discover the x-intercept
-2x +y = 2
if y = 0, then
-2x + 0 = 2
-2x = 2
-2x = 2
x = -1
x-intercept = -1 (-1, 0)
-2 -2
Discover the x-intercept
-2x + y = 4
if y = 0, then
-2x + 0 = 4
-2x = 4
-2x = 4
x = -2
x-intercept = -2
(-2, 0)
-2 -2
Place the x-intercept and y-intercept points on the graph to create linear line
4
-4
Equation #1:
(a, 0) = (-1, 0)
(0, b) = (0, 2 )
-2
4
-2
2
2
Equation #2:
(0, b) = (0, 4)
(a, 0) = (-2, 0)
4
-4
-2
4
2
2
SECOND STEP: DISCOVER THE SLOPE
SLOPE FORMULA
Discover the slope from the two intercepting points
Discover the slope
Discover the slope
if,
y-intercept (0, 2) &
x-intercept (-1, 0)
then,
0 - 2 -2
-1 - 0 -1
m = rise
run
m = =
if,
y-intercept (0, 4) &
x-intercept (-2, 0)
then,
0 - 4 -4 -2
-2 - 0 -2 -1
m = rise
run
m = = =
Draw the slope for each graph. This assist in ensuring the right linear direction.
Equation #1:
2 units
1 unit
(-1, 0)
(0, 2 )
4
-2
2
2
-2
-4
4
Equation #2:
(0, 4)
(-2, 0)
4
-2
4
2
2 units
1 unit
P (-1, 3)
-4
SOLUTION
Discovering the x & y-intercept & slope is a way of solving a system of equations.
Rule:
Both slopes are equal
Both y-intercepts are not equal
Equation #2
-2x + y = 4
m = -2
1
Equation #1
-2x + y = -2
m = -2
1
4
2
2
-2
-4
4
Equation #1
slope = -2/-1 = -2
y-intercept = (0, 2)
Equation #2
slope = -2/1 = -2
y-intercept = (0, 4)
Solution: None
Parallel equations have lines that do not intercept at any point.
The slope are equal.
The y-intercept are not equal.
The two linear lines are interdependent system of equations.
The y-value cannot depend on x-value to solve the equation, therefore, the equations are inconsistent.
Graphically these linear lines
DO NOT INTERSECT
thus, there is
NO solution
You are observing
parallel lines.
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