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EQUATION OF
THE LINE
USINGTWO INTERCEPT FORM
Jessebel G. Bautista
Antonio J. Villegas Voc’l High School
My
Profile
OBJECTIVES:
1.determine the values of
the variables
2.use two intercept 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. (6, 0) and (0, -2)
Solution:
Let
a = 6
b = -2
Use two intercept form since
x and y intecepts are given.
Find the equation of the line that passes through the
following points.
𝑥
6
+
𝑦
−2
= 1
{
𝑥
6
+
𝑦
−2
= 1 } 6
x - 3y = 6 or
-3y = -x + 6
y =
1
3
x + 2
𝑥
𝑎
+
𝑦
𝑏
= 1
EXAMPLE 2
2. (4, 0) and (0, 4)
Solution:
Let
a = 4
b = 4
Use two intercept form since x
and y intecepts are given.
Find the equation of the line that passes through the
following points.
𝑥
4
+
𝑦
4
= 1
{
𝑥
4
+
𝑦
4
= 1 } 4
x + y = 4 or
y = -x + 4
𝑥
𝑎
+
𝑦
𝑏
= 1
EXAMPLE 3
3. (4,0) and (0, 2)
Solution:
a = 4
b = 2
Use two intercept form since
x and y intecepts are given.
Find the equation of the line that passes through the
following points.
𝑥
4
+
𝑦
2
= 1
{
𝑥
4
+
𝑦
2
= 1 } 4
x + 2y = 4
𝑥
𝑎
+
𝑦
𝑏
= 1
TO DO …
1. (9,0) & (0, -5)
2. (3,0) & (0, 2)
3. (4,0) & (0,1)
4. (-7, 0) & (0, -3)
5. ( 4, 0) & (0, -2)
6. (8, 0) & (0, -3)
7. ( -5, 0) & (0 , 4)
8. (11, 0) & (0, -9)
9. (-6, 0) & (0, -2)
10. (4, 0) & (0, -6)
Find the equation of the line that passes through the
following points.
SALAMAT PO!!!
Learning Resources:
Grade 8 Math Time
k-to-12-grade-8-math-learner-module
Learning Resources:

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two intercept 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 intercept 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. (6, 0) and (0, -2) Solution: Let a = 6 b = -2 Use two intercept form since x and y intecepts are given. Find the equation of the line that passes through the following points. 𝑥 6 + 𝑦 −2 = 1 { 𝑥 6 + 𝑦 −2 = 1 } 6 x - 3y = 6 or -3y = -x + 6 y = 1 3 x + 2 𝑥 𝑎 + 𝑦 𝑏 = 1
  • 8. EXAMPLE 2 2. (4, 0) and (0, 4) Solution: Let a = 4 b = 4 Use two intercept form since x and y intecepts are given. Find the equation of the line that passes through the following points. 𝑥 4 + 𝑦 4 = 1 { 𝑥 4 + 𝑦 4 = 1 } 4 x + y = 4 or y = -x + 4 𝑥 𝑎 + 𝑦 𝑏 = 1
  • 9. EXAMPLE 3 3. (4,0) and (0, 2) Solution: a = 4 b = 2 Use two intercept form since x and y intecepts are given. Find the equation of the line that passes through the following points. 𝑥 4 + 𝑦 2 = 1 { 𝑥 4 + 𝑦 2 = 1 } 4 x + 2y = 4 𝑥 𝑎 + 𝑦 𝑏 = 1
  • 10. TO DO … 1. (9,0) & (0, -5) 2. (3,0) & (0, 2) 3. (4,0) & (0,1) 4. (-7, 0) & (0, -3) 5. ( 4, 0) & (0, -2) 6. (8, 0) & (0, -3) 7. ( -5, 0) & (0 , 4) 8. (11, 0) & (0, -9) 9. (-6, 0) & (0, -2) 10. (4, 0) & (0, -6) Find the equation of the line that passes through the following points.
  • 12. Learning Resources: Grade 8 Math Time k-to-12-grade-8-math-learner-module Learning Resources: