Slope and Linear Equations Algebra I

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

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

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

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

Graphs Positive Slope Negative Slope

Graphs Zero Slope Undefined Slope

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

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 =

Now you try -3x – 5y = 6

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

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

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

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

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 = -3 y – 5 = -3(x – 0) (6,-2), horizontal line y + 2 = 0(x – 6)

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

Standard Form Write each in standard form. 2y =-6x – 3 6x + 2y = -3 3x + 9y = 15 x + 3y = 5

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)

Slope Intercept Form Write the following in slope intercept form. 4x + 2y = 8 y = -2x + 4 -6x – 3y = 48 y = -2x - 16 Y – 8 = ⅛(x – 5) y = ⅛x + Y + 2 = ¾(x + 12) y = ¾x + 7

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

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

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

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

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

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

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.

Horizontal Line