1. The document discusses various forms of linear equations including standard form (Ax + By = C), slope-intercept form (y = mx + b), and point-slope form (y - y1 = m(x - x1)). 2. It provides examples of transforming linear functions between these forms and discusses how to find the slope and y-intercept of a linear function from its graph. 3. The slope and direction of a linear function's graph is determined by whether its slope is positive or negative. A positive slope produces an upward rising line while a negative slope produces a downward falling line.

1. Line & Its Slope

2. STANDARD FORM OF LINEAR EQUATION
Ax + By = C
Transform each linear function in standard form.
1. y = -9x + 2
9x + y = 2
2. y = 3/2 – 2x
2 (y = 3/2 – 2x) 2
2y = 3 – 4x
4x + 3y = 3

3. STANDARD FORM OF LINEAR EQUATION
Ax + By = C
3.
𝟐𝒙
𝟑
-
𝒚
𝟒
= 1 4. y -
𝟏
𝟐
= 2(x + 1)
12 (
𝟐𝒙
𝟑
-
𝒚
𝟒
= 1) 12
8x - 3y = 12
y -
𝟏
𝟐
= 2x + 2
2 (y -
𝟏
𝟐
= 2x + 2) 2
2y - 𝟏= 4x + 4
-4x + 2y = 4+1
-1(-4x + 2y = 5)-1 4x - 2y = -5

4. SLOPE – INTERCEPT FORM
y = mx + b
Transform each linear function in slope intercept form. Then,
identify the value of m and b.
1. 4x - y = 1
2. 2x + 3y = 6
3.
𝟑
𝟐
x +
𝟏
𝟑
y + 1 = 0
4.
𝒙
𝟐
+
𝒚
𝟓
= 3

5. Linear Equation
Graph each linear function.
1. y = 3x - 2
X -1 0 2
y

6. SLOPE OF A LINE
If 𝑷 𝟏 𝒙 𝟏, 𝒚 𝟏 𝒂𝒏𝒅𝑷 𝟐 𝒙 𝟐, 𝒚 𝟐 are points of the line
representing the linear function y = mx + b, then the
slope m of the line is
m =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
=
𝒚 𝟏−𝒚 𝟐
𝒙 𝟏−𝒙 𝟐

7. SLOPE OF A LINE
Determine the slope of the linear functions that passes
through the given pairs of points. Then draw the graph
of the linear functions.
1. (3,2) , (5,6) 2. (-2,0) , (1,-2)

8. The Slope, the trends and the graph of
linear function
If the slope is positive, the graph of a linear
function points upward to the right, and the
linear function increases all throughout.

9. The Slope, the trends and the graph of
linear function
If the slope is negative, the graph of a linear
function points upward to the left, and the
linear function decreases all throughout.

10. The Point – Slope Form
If the graph of a linear function y has a slope and
passes through 𝒙 𝟏, 𝒚 𝟏 , then its equation is
𝒚 − 𝒚 𝟏 = m(𝒙 − 𝒙 𝟏)

11. The Point – Slope Form
Write the equation of the linear function y in slope-
intercept form and in standard form whose graph
passes through the given point and has given slope m.
1. (-1,2) , m = 2 2. (3,-2) , m = -
𝟑
𝟐

12. The Two - Point Form
If the graph of a linear function passes through the
points 𝒙 𝟏, 𝒚 𝟏 and 𝒙 𝟐, 𝒚 𝟐 , then its equation is
𝒚 − 𝒚 𝟏 =
𝒚 𝟐−𝒚 𝟏
𝒙 𝟐−𝒙 𝟏
(𝒙 − 𝒙 𝟏)

13. Write the equation of the linear function y in slope-
intercept form and in standard form whose graph
passes through the given pairs of points.
1. (5,-4) , (-3,0) 2. (-4,3) , (5,-2)
The Two - Point Form

14. The Intercept Form
If the graph of a linear function has x-intercept a and y-
intercept b , then its equation is
𝒙
𝒂
−
𝒚
𝒃
= 𝟏

15. Write the equation of the linear function y in slope-
intercept form and in standard form whose graph has
given x-intercept a and y-intercept b.
1. a = 2 , b = -3 2. a =
−𝟏
𝟐
, 𝒃 =
−𝟐
𝟑
The Two - Point Form