Slope Homework

/ @ ALgebra

_~Finding the Slope of a Line You are already familiar with the concept slope. When you walk uphill, you walk up a slope. When you walk downhill, you walk d wn a slope. A graphed line, like a hill, has a slope. The slope of a line is given as a number. When you move been two points on the line, the slope is found by dividing the chang value by the corresponding change in x value.

• A line that goes up from left to right has a poive slope. • A line that goes down from left to right has ~egative slope. In Example 1, the slope of the line is 2.

In; xample 2, the slope of the line is -(

EXRMPLE1

JMPLE 2

Slope

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The line above has positive sLop because it goes up from left to ght.

The line above has negative sLope because it goes down from left to right. Y

Zero Slope and Undefined Slope Two types of lines have neither posi e nor negative slope. • A horizontal line has zero sl£ e. The x-axis (or any horizontalliq ) is a line with 0 slope. • A vertical line has an undefi ed slope. The concept of slope does t >tapply to a vertical line. The y-axis (or .'.ny vertical line) isa line with undefine, slope.

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Graphing

1. Name the slope of each line as positive, negative, zero, or undefined. y

Equations

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2. Find the numerical value of the slope of line E. Identify the x- and y-intercepts. Y

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Slope of line E is

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3. Find the numerical value of the slope of line F. Identify the x- and y-intercepts.

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4. Subtract the coordinates to find the slope of the line that passes through each pair of points. Part a is done as an example. a.

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@ Algebra

JGraphing a Linear Equation When solutions of a linear equation such as y = 3x - 1 are plotted on a coordinate grid, they always lie on a straight line. Drawing this line of solutions is called graphing the equation. To graph a linear equation, follow these steps. STEP 1

Choose three vaLues for x and find the matching vaLues for y. Write each pair of vaLues in a TabLeof VaLues.

STEP 2

PLotthe three points on a coordinate grid; then connect them with a Line extending to the edges of the grid.

Graph the equation y = 3x - 1. STEP 1

Let x

= 0,

1, and 2. SoLvethe equation 1 for these three vaLues. Make a TabLeof VaLues.

y

= 3x -

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value

y= 3x.~ 1.

x

Y

x=O

y=3(0)-1=-1

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x=l

= 3(1) Y = 3(2)

- 1=2

1

2

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2

5

x

Y

x=2

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Table of Values

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1. y=x-2

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Graph each equation. As a first step, complete the Table of Values. Then find the x- and y-intercepts and slope for each graphed line.

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PLotthe points A = (0, -1) B = (1, 2) C = (2, 5). Conne.ct them with a Line that extends to the edges of the grid.

STEP 2

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