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Slope and Linear Equations Algebra I

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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

EquationsSlope 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

12

12

xx

yy

Equations

Point-slope y - = m(x - )

Leave the ‘x’ as ‘x’ and the ‘y’ as ‘y’

1x 1y

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 = 4A=9B=-5C=4 Object is to get ‘y’ by itself!

Example:

9x – 5y = 4Take away the term with the x -5y = -9x + 4Divide 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.1) (3,5), m =2) (-2,0), m = -3) (-3,2), m = -½4) (0,5), m = -3 5) (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.1) (3,5), m = y – 5 = (x – 3)2) (-2,0), m = - y – 0 = - (x + 2)3) (-3,2), m = -½ y – 2 = -½(x + 3)4) (0,5), m = -3 y – 5 = -3(x – 0)5) (6,-2), horizontal line y + 2 = 0(x –

6)

Standard Form

Write each in standard form.1) 2y = -6x – 32) Y = ¾x – 53) Y = -⅜(x + 12)4) Y = 4x – 35) 4y = 2x + 126) 3x + 9y = 15

Standard Form

Write each in standard form.1) 2y =-6x – 3 6x + 2y = -3

2) Y = ¾x – 5 3x – 4y = 203) Y = -⅜(x + 12) ⅜x + y = -4) Y = 4x – 3 4x – y = 35) 4y = 2x + 12 x + -2y = -66) 3x + 9y = 15 x + 3y = 5

Slope Intercept Form

Write the following in slope intercept form.1) 4x + 2y = 82) -6x – 3y = 483) Y – 8 = ⅛(x – 5)4) Y + 2 = ¾(x + 12)

Slope Intercept Form

Write the following in slope intercept form.1) 4x + 2y = 8 y = -2x + 42) -6x – 3y = 48 y = -2x - 163) Y – 8 = ⅛(x – 5) y = ⅛x + 4) Y + 2 = ¾(x + 12) y = ¾x + 7

Slope

Find the slope from the sets of points.1) (5,8) and (-3,7)2) (5,-2) and (3, -2)3) (-2,-5) and (8,-3)4) (-3,-3) and (-3,1)

Slope

Find the slope from the sets of points.1) (5,8) and (-3,7) m = ⅛2) (5,-2) and (3, -2) m = 03) (-2,-5) and (8,-3) m = 4) (-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 = -2X = 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 lineX = 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