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EQUATION OF
THE LINE
USING TWO POINT FORM
Jessebel G. Bautista
Antonio J. Villegas Voc’l High School
My
Profile
OBJECTIVES:
1.determine the values of
the variables
2.use two point form
3.substitute the given
values
4.find the equation of a
line
Mathematical Concepts:
Two Intercept Form
where a and b are x and y intercepts of the line
respectively.
𝑥
𝑎
+
𝑦
𝑏
= 1
Mathematical Concepts:
The Point-Slope Form
given a slope and a point of a line, we may find the
equation by substituting their respective values in
the point-slope form.
y - y1 = m (x - x1)
Mathematical Concepts:
The Two-Point Form
given two points of a line determine the values of x1, y1, x2,
and y2 then substitute it to the two-point form to find the
equation of the line.
y - y1 =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
(x - x1)
EXAMPLE 1
1. (8, 5), (6, 1)
Solution:
Let x1 = 8 x2 = 6
y1 = 5 y2 = 1
Substitute assigned values to the
two-point form.
Find the equation of a line that passes through the following points.
Express the equation in the slope-intercept form.
y - 5 =
1−5
6−8
(x - 8)
y - 5 =
−4
−2
(x - 8)
y - 5 = 2(x - 8)
y - 5 = 2x - 16
y = 2x -11
y - y1 =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
(x - x1)
EXAMPLE 2
2. (5, 6), (7, -4)
Solution:
Let x1 = 5 x2 = 7
y1 = 6 y2 = -4
Substitute assigned values to the
two-point form.
Find the equation of a line that passes through the following points.
Express the equation in the slope-intercept form.
y - 6 =
−4−6
7−5
(x - 5)
y - 6 =
−10
2
(x - 5)
y - 6 = -5(x - 5)
y - 6 = -5x + 25
y = -5x + 31
y - y1 =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
(x - x1)
EXAMPLE 3
3. (5, 3), (3, 1)
Solution:
Let x1 = 5 x2 = 3
y1 = 3 y2 = 1
Substitute assigned values to the
two-point form.
Find the equation of a line that passes through the following points.
Express the equation in the slope-intercept form.
y - 5 =
1−3
3−5
(x - 5)
y - 5 =
−2
−2
(x - 5)
y - 5 = 1(x - 5)
y - 5 = x - 5
y = x + 0
y = x
y - y1 =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
(x - x1)
TO DO …
1. (9,6) & (7, -5)
2. (0,3) & (1,0)
3. (4,3) & (2,1)
4. (-7, 1) & (1, -3)
5. ( 4, -3) & (-2, 1)
6. (8, 6) & (8, -3)
7. ( -5, 1) & (-6 , 4)
8. (11, -7) & (6, -9)
9. (-6, -4) & (-10, -2)
10. (4, -6) & (1, -6)
Find the equation of the line that passes through the following
given points. Express the equation in slope-intercept form.
SALAMAT PO!!!
Learning Resources:
Grade 8 Math Time
k-to-12-grade-8-math-learner-module
Learning Resources:

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equation of the line using two point form

  • 1. EQUATION OF THE LINE USING TWO POINT FORM
  • 2. Jessebel G. Bautista Antonio J. Villegas Voc’l High School My Profile
  • 3. OBJECTIVES: 1.determine the values of the variables 2.use two point form 3.substitute the given values 4.find the equation of a line
  • 4. Mathematical Concepts: Two Intercept Form where a and b are x and y intercepts of the line respectively. 𝑥 𝑎 + 𝑦 𝑏 = 1
  • 5. Mathematical Concepts: The Point-Slope Form given a slope and a point of a line, we may find the equation by substituting their respective values in the point-slope form. y - y1 = m (x - x1)
  • 6. Mathematical Concepts: The Two-Point Form given two points of a line determine the values of x1, y1, x2, and y2 then substitute it to the two-point form to find the equation of the line. y - y1 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (x - x1)
  • 7. EXAMPLE 1 1. (8, 5), (6, 1) Solution: Let x1 = 8 x2 = 6 y1 = 5 y2 = 1 Substitute assigned values to the two-point form. Find the equation of a line that passes through the following points. Express the equation in the slope-intercept form. y - 5 = 1−5 6−8 (x - 8) y - 5 = −4 −2 (x - 8) y - 5 = 2(x - 8) y - 5 = 2x - 16 y = 2x -11 y - y1 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (x - x1)
  • 8. EXAMPLE 2 2. (5, 6), (7, -4) Solution: Let x1 = 5 x2 = 7 y1 = 6 y2 = -4 Substitute assigned values to the two-point form. Find the equation of a line that passes through the following points. Express the equation in the slope-intercept form. y - 6 = −4−6 7−5 (x - 5) y - 6 = −10 2 (x - 5) y - 6 = -5(x - 5) y - 6 = -5x + 25 y = -5x + 31 y - y1 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (x - x1)
  • 9. EXAMPLE 3 3. (5, 3), (3, 1) Solution: Let x1 = 5 x2 = 3 y1 = 3 y2 = 1 Substitute assigned values to the two-point form. Find the equation of a line that passes through the following points. Express the equation in the slope-intercept form. y - 5 = 1−3 3−5 (x - 5) y - 5 = −2 −2 (x - 5) y - 5 = 1(x - 5) y - 5 = x - 5 y = x + 0 y = x y - y1 = 𝒚 𝟐−𝒚 𝟏 𝒙 𝟐−𝒙 𝟏 (x - x1)
  • 10. TO DO … 1. (9,6) & (7, -5) 2. (0,3) & (1,0) 3. (4,3) & (2,1) 4. (-7, 1) & (1, -3) 5. ( 4, -3) & (-2, 1) 6. (8, 6) & (8, -3) 7. ( -5, 1) & (-6 , 4) 8. (11, -7) & (6, -9) 9. (-6, -4) & (-10, -2) 10. (4, -6) & (1, -6) Find the equation of the line that passes through the following given points. Express the equation in slope-intercept form.
  • 12. Learning Resources: Grade 8 Math Time k-to-12-grade-8-math-learner-module Learning Resources: