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The point-slope form of a linear equation of a non-vertical line is given by:
Point-Slope Form of a Linear Equation
1 1y y m x x
1 1
is the slope of the line
is a point on the line
,
m
x y
Example 1: Write the point-slope form equation of the3
4.mline that contains the point (3, -5) and has slope
1 1y y m x x
Substitute values into the equation …
Slope: 1 1
3
4y y x x
3
4.m
Simplify:
35 3
4y x
Point:
3, 5
1 1,x y
3
45 3y x
1 1
3
4y y x x
Example 2: Write the slope-intercept equation of
2.
5m
the line that contains the point (- 2, 5) and has slope
First, substitute the given point and slope values into the point-slope equation.
1 1y y m x x
55 2
2y x
Simplify 55 2
2y x
Next, put in slope-intercept form, y mx b
55 2
2y x
55 2
2y x 2
22
Multiply each term by the common denominator …
2 10 5 2y x
Simplify and solve for y
2 10 5 2y x
2 10 5 10y x
2 5 20y x
510
2y x
Example 3: Write the slope-intercept equation of the line that contains the points (- 1, 8) and (4, - 2).
First, find the slope of the line using the given points.
m 2 1
2 1
y y
x x
2 8
4 1
10
5
2
Next, substitute either given point (let’s use (- 1, 8)) and the slope, - 2, into the point-slope equation.
Last, simplify and write in slope-intercept form.
8 2 1y x
8 2 1y x
8 2 2y x
2 6y x