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.
