Learning Competencies
1. illustrates and finds the slope of a line given two points, equation, and graph
2. writes the linear equation ax + by = c to in the form y = mx + b and vice versa
3. graphs a linear equation given (a) any two points; (b) x – and y – intercepts; (c) the
slope and a point on the line
4. describes the graph of a linear equation in terms of its intercepts and slope
5. finds the equation of a line (a) two points; (b) the slope and a point; (c) the slope and its
intercepts
Slope
The slope of a line is a measure of the steepness of the
line.
Given two points on a line, the slope is the ratio of the
vertical change or rise between the points and the
horizontal change or run between the points. The symbol
for slope is m.
𝑚= rise
run
Slope Formula
The slope of a line containing two points (𝑥1, 𝑦1), is given by
𝑦2 − 𝑦1
Slope = m =
; 𝑥1 ≠ 𝑥2
𝑥2− 𝑥1
Example 1: Find the slope of the line containing
the points (2,5) and (-3,7).
Solution:
Example 1: Find the slope of the line containing
the points (2,5) and (-3,7).
Solution:
Let (2,5) be (𝑥1, 𝑦1) and (-3,7) be (𝑥2,𝑦2),
then by definition of slope,
𝑦2− 𝑦1
𝑚=
𝑥2− 𝑥1
−( )
7−5
=
=
=
−( )
−3−2
2
−2
−5
=
5
Example 2: Find the slope of the line containing
the points (5,8) and (2,3).
Solution:
Example 2: Find the slope of the line containing
the points (5,8) and (2,3).
Solution:
Let (5,8) be (𝑥1, 𝑦1) and (2,3) be (𝑥2,𝑦2),
then by definition of slope,
𝑦2− 𝑦1
𝑚=
𝑥2− 𝑥1
−( )
3−8
=
=
=
−( )
2−5
−5
5
−3
=
3
Example 3: Find the slope of the line containing
the points (3,4) and (-2,4).
Solution:
Example 3: Find the slope of the line containing
the points (3,4) and (-2,4).
Solution:
Let (3,4) be (𝑥1, 𝑦1) and (-2,4) be (𝑥2,𝑦2),
then by definition of slope,
𝑦2− 𝑦1
𝑚=
𝑥2− 𝑥1
−( )
4−4
=
=
=
−( )
0
−5
=0
−2−3
Example 4: Find the slope of the line containing
the points (-5,8) and (-5,3).
Solution:
Example 4: Find the slope of the line containing
the points (-5,8) and (-5,3).
Solution:
Let (-5,8) be (𝑥1, 𝑦1) and (-5,3) be (𝑥2,𝑦2),
then by definition of slope,
𝑦2− 𝑦1
𝑚=
𝑥2− 𝑥1
−( )
=
=
3−8
−( )
−5−(−5)
−5
=
= undefined
0
Equation of a Line
Equation of a Line
Equation of a Line
1. (2, 5) and (-3, 7)
2. (5, 8) and (2, 3)
3. (3, 4) and (-2, 4)
4. (-5, 8) and (-5, 3)