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One important feature is that it easily identifies the slope and y-intercept.
Anchor 1
It is needed to discover a linear equation line.
Its' graph forms a straight line.
Slope-intercept equations can quickly determine the slope & y-intercept of a linear line.
It can also be utilized to find the x-intercept.
It is derived from the point-slope formula.
It is often equated with Ax + By + C = 0.
SLOPE-INTERCEPT FORMULA
Components of the slope-intercept format
y = mx + b
output
slope
y = mx + b
input
y-intercept
Convert point-slope format to slope-intercept format
1)
Discover the slope, if unknown
1
=
(y - y )
m
x
1
(x - )
2
=
1
(y - y )
(x - x )
2
1
m
( )
1
x - x
2
1
x - x
2
m =
1
y - y
2
1
x - x
2
2)
Slope-intercept from point-slope
1
=
(y - y )
m
x
1
(x - )
y -
1
1
(y + y )
=
m
+ y
1
1
x
(x - )
y =
mx -
1
mx
1
+ y
y =
1
1
( y - mx )
mx +
3)
(y - mx ) = y = y- intercept = b
1
1
4)
y = mx + b
1
Slope-Intercept Formula
Explanation of creating the slope-intercept formula from a point and slope
Given, the slope and 1 point:
slope: 3
point: (-1, 4)
Write in slope-intercept format:
y = mx + (y - mx )
y = 3x + (4 - (3)(-1))
y = 3x + 4 + 3
y = 3x + 7
1
Write in slope-intercept format:
y = mx + (y - mx )
y = 4x + (5 - (4)(2))
y = 4x + 5 - 8
y = 4x - 3
1
Given, the slope and 1 point:
slope: 4
point: (2, 5)
Slope-Intercept Formula
Examples of creating the slope-intercept formula from a point and slope
Given, the slope and 1 point:
slope: 2
point (x, y): (3, 5)
Discover the y-intercept
What is the y-intercept?
y = mx + b --substitute 2 for slope=m
y = 2x + b --substitute 3 for x & 5 for y
5 = 2(3) + b --multiply rule
5 = 6 + b
5 - 6 = 6 - 6 + b --subtract 6 from both sides
-1 = b --y-intercept
Substitute the slope, and y-intercept
into the slope-intercept equation:
m: 2
b: -1
Slope-intercept form:
y = mx + b
y = 2x -1
Given, the slope and 1 point:
slope: 2
point (x, y): (-3, 1)
Discover the y-intercept
What is the y-intercept?
y = mx + b --substitute 2 for slope=m
y = 2x + b --substitute -3 for x & 1 for y
1 = 2(-3) + b --multiply rule
1 = -6 + b
1 + 6 = -6 + 6 + b --subtract 6 from both sides
7 = b --y-intercept
Substitute the slope, and y-intercept
into the slope-intercept equation:
m: 2
b: 7
Slope-intercept form:
y = mx + b
y = 2x + 7
Slope-Intercept Formula
Explanation of discovering the slope and y-intercept from the slope-intercept
The slope and y-intercept can easily be observed in the formula:
Given, the slope-intercept form:
y = mx + b
y = -2x + 3
What is the slope?
-2
What is the y-intercept (b)?
if x = 0
y = -2(0) + 3
y = 0 + 3
y = 3
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