types of slope slope - wpmu dev

Unit 5 Smart Notes & TOC.notebook

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February 14, 2019

58 Types of slope 59 Calculating slope from a graph 60 Calculating slope from two points 61 Calculating slope from a table 62 Graphing from slope intercept form 63 Solving for y & standard form 64 Graphing from standard form 65 Graphing lines from tables 66 Graphing special cases 67 Writing equations from graphs 68 Writing equations from slope & a point 69 Writing equations from two points


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TYPES OF SLOPE

The SLOPE of a line is the "slant" of a line or its steepness.It is also called R_______________ of C_________________.

A line with a ___________________ SLOPE slants "uphill" or rises from left to right.

A line with a ___________________ SLOPE slants "downhill" or falls from left to right.

positive or negative positive or negative positive or negative


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February 14, 2019

A ______________________ line will have an __________________ slope.

A ______________________ line will have a slope of ________________ .

y = 1 slope = 0


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February 14, 2019

Let's draw "Mr. Slope" to help us remember the types of slopes.


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February 14, 2019

CALCULATING SLOPE from a GRAPH

Slope is denoted by using the letter _____ .

Slope = rise = _____________ change = change in y = ∆y ____ horizontal change change in __ ∆x

SLOPE FROM A GRAPH

m = _____ m = _____

m = _____ m = _____

m = _____ m = _____


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February 14, 2019

CALCULATING SLOPE from TWO POINTS

SLOPE FORMULA m = y2 y1 x2 x1

STEPS:1.) Label the two sets of points with (___ , y1) and (x2, ___).2.) Write the _____________________________ formula.3.) _________________________ numbers WITH SIGNS into the formula.4.) Simplify your ratio/fraction.


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Examples:

a) (1, 5) and (3, 3) b) (3, 6) and (1, 8)

m = _____ m = _____

c) (4, 1) and (4, 7) d) (0, 5) and (2, 5)

m = _____ m = _____

e) (3, 6) and (2, 6) f) (4, 5) and (8, 1)

m = _____ m = _____


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February 14, 2019

CALCULATING SLOPE from a TABLESteps:1.) Pick any two ordered pairs from the table.2.) Label the two sets of points with (___ , y1) and (x2, ___).3.) Write the _____________________________ formula.4.) _________________________ numbers WITH SIGNS into the formula.5.) Simplify your ratio/fraction.

a) x y b) x y c) x y 0 6 3 18 0.75 1.24 1 8 6 12 0.4 1.84 2 10 9 6 0.05 2.44 3 12 12 0 0.3 3.04

m = ____ m = ____ m = ____

d) Min $ e) Hrs Miles f) Hrs. $ 10 5 15 550 5 13.75 20 6.50 18 925 7 20.25 30 8 21 1300 9 26.75 40 9.50 24 1675 11 33.25

m = ____ m = ____ m = ____


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February 14, 2019

GRAPHING from SLOPE INTERCEPT FORM

Slope Intercept Form is when we have an equation in the formy = mx + b

"M" is the _________________________________ of the line."B" is the ___________________________________________ .

The yintercept/b is the yvalue when x = 0. It is the point where the graph crosses the yaxis.

"B" tells you where the BEGIN! "M" tells you where to MOVE!


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February 14, 2019

1.) y = 2x 3 b = ___ 2.) y = 1/4 x + 1 b = ___ m = ___ m = ___

3.) y = 4x b = ___ 4.) y = 3x + 2 b = ___m = ___ m = ___

5.) y = 3/4 x 4 b = ___ 6.) y = x + 3 b = ___m = ___ m = ___


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February 14, 2019

SOLVING FOR Y & STANDARD FORM

STANDARD FORM of an equation has the "x" and the "y" on hte same side of the equation. 2x + 5y = 8

In order to graph this line, we have to convert the equation to SLOPE INTERCEPT FORM y = mx + b. In other words, we have to

SOLVE for Y.Steps:1.) Move the "x" term to the right side by doing the inverse on both sides.2.) Divide both sides by the coefficient in front of the "y," so now the "y" is alone on the left side.


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February 14, 2019

Examples:

a) x + y = 5 b = ____ b) 4x + y = 1 b = ___m = ____ m = ___

c) 2x + 3y = 12 b = ____ d) 3x = 2y b = ___m = ____ m = ___


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February 14, 2019

GRAPHING from STANDARD FORM

Rewrite the equation in slopeintercept form (y = mx + b), then graph using the yintercept (b) and the slope (m).

1.) x 2y = 8 * Solve for y!

b = ____m = ____

2.) 6x 3y = 3

b = ____m = ____

3.) 5y = 15x

b = ____m = ____

4.) 2x y = 3

b = ____m = ____


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February 14, 2019

GRAPHING LINES from TABLES

If given a table and an equation, follow these steps:1.) Rewrite the equation in slopeintercept form (y = mx + b).2.) Substitute the given inputs/xvalues, and solve for the outputs/yvalues.3.) Graph using AT LEAST THREE sets of ordered pairs to make sure you have a straight line.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

a) 6x + 2y = 10 x y 1 0 1 2

y = __________

b) 8x 4y = 16 x y 1 0 1 2

y = __________


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February 14, 2019

GRAPHING SPECIAL CASES

Special Cases are graphs with either: * Slope = ZERO; a _________________________________ line * UNDEFINED slope; a _____________________________ line

Examples:

a) x = 4 * Find 4 on the xaxis * Draw a ______________________ line because every number on that line has an xvalue of 4.

b) y = 3 * Find 3 on the yaxis * Draw a ______________________ line because every number on that line has an yvalue of 3.

c) x = 1 * Find 1 on the xaxis * Draw a ______________________ line because every number on that line has an xvalue of 1.


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February 14, 2019

WRITING EQUATIONS from GRAPHS

Slope Intercept Form y = ____ x + ____

_______ ______________

Write an equation given the slope and the yintercept.1) slope = 5, yintercept = 2 equation: _______________

2) slope = 1/2 , yintercept = 3 equation: _______________

3) slope = 0, yintercept = 1 equation: _______________


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February 14, 2019

4) 5)

Equation: _______________ Equation: _______________

6) 7)

Equation: _______________ Equation: _______________


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February 14, 2019

WRITING EQUATIONS from SLOPE & a POINTSteps:1.) Write the slope intercept equation (y = mx + b)2.) Substitute slope in for "m" and the ordered pair in for (x,y)3.) Solve for b (the yintercept)4.) Substitute the slope (m) and the yintercept (b) back into the equation5.) Keep the "x" and the "y" in the equation do NOT put numbers in the "x" and the "y" spots.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

a) Write the equation if the slope is 2 and the line goes through point (2, 3).

b) Slope = 1/2 and (4, 3)


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February 14, 2019

WRITING EQUATIONS from TWO POINTS

Steps:1.) Use the slope formula m = y2 y1 x2 x1 to calculate the slope.2.) Write the slope intercept equation (y = mx + b).3.) Choose ONE of the ordered pairs.4.) Substitute the ordered pair AND the slope into y = mx + b.5.) Solve for the yintercept (b).6.) Substitute the slope (m) and yintercept (b) back into the equation. Do NOT put numbers in for x and y!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

a) Write the equation of a line which passes through (2, 3) & (4, 5). Slope Solve for b Equation m = y2 y1 (y = mx + b) (y = mx + b) x2 x1

b) (4, 2) & (2, 3) Slope Solve for b Equation m = y2 y1 (y = mx + b) (y = mx + b) x2 x1

types of slope slope - wpmu dev

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