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The components are a pair of x and y-coordinates and the slope of a linear line.
Point-slope is one of many ways of solving a linear equation.
It can be solved with one or two points, along with the slope.
It assist in discovering a point on a line, when you have a point and the slope.
POINT-SLOPE FORMULA
Components of the point-slope formula
y - y = m(x - x )
1
1
known points
slope
1
1
y - y = m (x - x )
any point
Convert slope to point-slope format
1)
Given,
m =
2
1
y - y
x - x
2
1
2)
m
2
1
(x - x )
=
*
x - x
2
1
y - y
2
1
x - x
2
1
3)
=
1
(y - y )
2
m
(x - x )
2
1
1
y & x are known points on the line then,
1
y
2
= y
x
= x
2
4)
x
1
=
m
(x - )
1
(y - y )
Point-Slope Formula
Example of writing a point-slope formula from two points
Given, 2 points:
A: (0, 3) = first point
B: (3, 4) = second point
What is the slope?
2
x = 0
x = 3
1
y = 3
y = 4
2
1
m =
2
1
y - y
x - x
2
1
=
4 - 3
=
3 - 0
1
3
Substitute any known point into the point-slope equation:
x
1
=
m
(x - )
1
(y - y )
Point A: (0, 3)
y - 3 = 1 ( x - 0)
3
(3, 4)
6
B
1
(y - y )
6
4
4
2
A
(0, 3)
1
(x - x )
-2
-2
2
-10
-8
-6
-4
-4
Point-slope form:
y - 3 = 1 ( x - 0)
3
OR
y - 3 = -1 x
3
Point-Slope Formula
Example of writing a point-slope formula from one point & a slope
Given, the slope is known:
m = 2
Given the points are known:
x = 3
y = 4
1
1
Substitute the numbers into the formula:
Point-slope form:
y - 4 = 2( x - 3)
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