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One important reason is that once plotted on a coordinate plane, it is easier to immediatley visualize and recognize a linear equation on the graph.
The x & y intercepts are basically numbers.
However, the intercepts of a line are when a point or curve passes the x or y axis.
The x-intercept is described as the x-value that coincides with the x-axis.
At the x-axis the y-value is zero and forms the coordiante pair, (X, 0).
The y-intercept is described as the y-value that coincides with the y-axis.
At the y-axis the x-value is zero and forms the coordiante pair, (0, Y).
X- INTERCEPT & Y-INTERCEPT
Explanation of the concept of x- & y-intercept
X-INTERCEPT
Rule:
if y= 0, then the x-intercept can be discovered
Y-INTERCEPT
Rule:
if x = 0 , then the y-intercept can be discovered
Slope-Intercept: X & Y Intercept
Explanation of discovering x- & y-intercept with the slope-intercept form
Discover the y-intercept
What is the y-intercept?
y = mx + b
When x = 0, then
Y-intercept:
y = m(0) + b
y = 0 + b
y = y-intecept = b --> (0,b)
Discover the x-intercept
What is the y-intercept?
y = mx + b
When y = 0, then
m m
X-intercept
​
0 = mx + b
-b + 0 = mx + b - b
-b = mx + b
x = x-intercept = b = -->(a, 0)
m
Linear line creates y = mx + b
(0, 0)
a
b
(0, b) = y-intercept
(a, 0) = x-intercept
Slope-Intercept: X & Y Intercept
Example of discovering x- & y-intercept with the slope-intecept form
Given, the slope-intercept equation
y = mx + b
y = -2x + 2
Discover the y-intercept
What is the y-intercept?
y-intercept: y = -2x + 2
y = (-2*0) + 2 --substitute 0 for x & multiply y = 0 + 2 --addition rule
y = 2 --> (0,b) --> (0, 2) --y-intercept
Discover the x-intercept
What is the x-intercept?
x-intercept: y = -2x + 2
0 = -2x + 2 --substitute 0 for y
0 - 2 = -2x + 2 - 2 --subtract 2 from both sides
-2 = -2x + 0
-2 = -2x --divide -2 from both sides
-2 = -2x --divide -2 from both sides
x = 2 --> (a, 0) --> (1, 0) --x-intercept
-2 -2
Standard Form: X & Y intercept
Explanation of discovering x- & y-intercept with the standard form
X-INTERCEPT
Rule:
x-intercept (a, 0) is when y = 0, and a value passes the x-axis
Y-INTERCEPT
Rule:
y-intercept (0, b) is when the x = 0, and a value passes the y-axis
Discover the y-intercept
What is the y-intercept?
Ax + By = C
Ax + By = C
Ax -Ax + By = C - Ax
0 + By = C - Ax
By = C - Ax
B B B
y = C + 0
B
b = C
B
y = y-intercept = C = b -->(0, b)
B
where, x = 0, then -Ax = 0 B
Discover the x-intercept
What is the x-intercept?
Ax + By = C
Ax + By = C
Ax -Ax + By = C - Ax
0 + By = C - Ax
0 = C - Ax
0 + C = - Ax
C = -Ax
-A -A
C = x
-A
x = x-intercept = C = a -->(a, 0)
-A
where, y = 0, then By = 0
m
(x - )
x
1
Standard Form: X & Y Intercept
Example of discovering x- & y-intercept with the standard form
Equation: 1x - 3y = -9
Given, the slope-intercept equation
Ax + By = C
1x - 3y = -9
Discover the y-intercept
What is the y-intercept?
--divide -3 on both sides
y-intercept: 1x - 3y = -9
0 - 3y = -9 --substitute 0 for y & multiply
- 3y = -9
-3 -3
y = 3 --> (0,3) --y-intercept
What is the x-intercept?
Discover the x-intercept
x-intercept: 1x - 3y = -9 1x - 3(0) = -9 --substitute 0 for y & multiply
1x - 0 = -9
1x = -9 1 1
x = 1 --> (1,0) --x-intercept
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