1. Slope and Linear Equations
Algebra I

2. Vocabulary Linear Equation – The equation of a line.
Y intercept – where the line crosses the y axis.
X intercept – where the line crosses the x axis.
GCF – greatest common factor

3. Equations Slope m = Slope Intercept y = mx + b
slope y - intercept
Direct Variation y = k x
constant of variation
Inverse Variation x y = k
Standard Ax + By = C

4. Equations
Point-slope y - = m(x - ) Leave the ‘x’ as ‘x’ and the ‘y’ as ‘y’

5. Rules for Standard Form
Standard Ax + By = C
‘A’ can’t be a negative or a fraction
Both ‘A’ & ‘B’ can’t be zero
‘A’, ‘B’ and ‘C’ are integers whose GCF is 1

6. Graphs
Positive Slope Negative Slope

7. Graphs
Zero Slope Undefined Slope

8. Examples: From standard to slope intercept: 9x – 5y = 4 A=9 B=-5 C=4
Object is to get ‘y’ by itself!

9. Example:
9x – 5y = 4 Take away the term with the x -5y = -9x + 4 Divide both sides by -5 y= x + This is your final answer! m = b =

10. Now you try
-3x – 5y = 6

11. Now you try
-3x – 5y = 6 +3x +3x -5y = 3x y = - x - m = - b = -

12. Finding the x intercept
To find the x intercept, make the y = 0 in the equation and solve for x.
3x + 7y = 24
3x + 7(0) = 24
3x = 24
x = 8

13. Finding the y intercept
To find the y intercept, make the x = 0 in the equation and solve for y.
4x – 2y = 36
4(0) – 2y = 36
-2y = 36
y = -18

14. Point-slope Form
Write point-slope form of an equation of a line that passes through the given point and slope.
(3,5), m =
(-2,0), m = -
(-3,2), m = -½
(0,5), m = -3
(6,-2), horizontal line

15. Point-slope Form
Write point-slope form of an equation of a line that passes through the given point and slope.
(3,5), m = y – 5 = (x – 3)
(-2,0), m = y – 0 = - (x + 2)
(-3,2), m = -½ y – 2 = -½(x + 3)
(0,5), m = y – 5 = -3(x – 0)
(6,-2), horizontal line y + 2 = 0(x – 6)

16. Standard Form Write each in standard form. 2y = -6x – 3 Y = ¾x – 5

17. Standard Form Write each in standard form. 2y =-6x – 3 6x + 2y = -3
3x + 9y = x + 3y = 5

18. Slope Intercept Form Write the following in slope intercept form.
4x + 2y = 8
-6x – 3y = 48
Y – 8 = ⅛(x – 5)
Y + 2 = ¾(x + 12)

19. Slope Intercept Form Write the following in slope intercept form.
4x + 2y = y = -2x + 4
-6x – 3y = y = -2x - 16
Y – 8 = ⅛(x – 5) y = ⅛x +
Y + 2 = ¾(x + 12) y = ¾x + 7

20. Slope Find the slope from the sets of points. (5,8) and (-3,7)

21. Slope Find the slope from the sets of points. (5,8) and (-3,7) m = ⅛
(-3,-3) and (-3,1) m = undefined
** when slope is undefined the answer will be x = (the given x value)
x = -3

22. Writing Equations
Write an equation when given a slope and y-intercept. m = 4, b = 8 m = -4, b = 0 Special equations: Y = -2 X = 4

23. Writing Equations
Write an equation when given a slope and y-intercept. m = 4, b = 8 y = 4x + 8 m = -4, b = 0 y = -4x (don’t need to write the zero) Special equations: Y = -2 graph as a horizontal line X = 4 graph as a vertical line

24. Identify Slope
When asked to identify slope, put in slope-intercept or point slope form. y = 3x + 15 Y – 5 = 4(x – 9) y = 7 x = -9

25. Identify Slope
When asked to identify slope, put in slope-intercept or point slope form. y = 3x + 15 m = 3 Y – 5 = 4(x – 9) m = 4 y = 7 no slope x = -9 undefined slope

26. Graphing Linear Equations
Always graph the y intercept first. That will be the ‘b’ in the equation, make a point on the y axis.
Starting with the y intercept, use the slope and graph “rise over run”.
The numerator is the ‘rise’.
The denominator is the ‘run’.
Rise up or down depending on a positive or negative slope.
Always ‘run’ to the right.

27. Horizontal Line