Slope of a Fitted Line

Slope of a Line

Prepare: pen and paper

Lesson Goals

• Answer prerequisite skills assessment.

• Answer guide questions in Let Us Connect channel.

• Study Slope of a Line.

• Answer Practice Exercises

PREREQUISITE SKILLS

Find the slope of each line.

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Find the slope. You may use "/" if your answer is in fraction form and use improper fraction.

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Find the slope. You may use "/" if your answer is in fraction form and use improper fraction.

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Find the slope. You may use "/" if your answer is in fraction form and use improper fraction.

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Find the slope. You may use "/" if your answer is in fraction form. Use improper fraction and/or reduce to lowest term.

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Find the slope. You may use "/" if your answer is in fraction form and use improper fraction.

End of Prerequisite Skills Assessment

Please answer Guide Questions found in Let Us Connect channel and study in advance the topic after this slide.

SLOPE OF A LINE

I can illustrate slope of a line and find the slope of a given line given two points, equations, and graphs.

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Practice Exercise #1:

Find the slope of a line that passes through the points (-3,1) and (-1,5).

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Practice Exercise #2:

Determine if the points (0,6), (2, 12), and (-3, -3) are collinear.

Answer Yes or No.

Slope and Intercepts: Direction and Trend

Activity #1.

In your paper, graph the following linear equations and observe the slope and the trend.

•  $y=3x-2$  

•  $8x-2y=4$  

•  $-7x+4y-8=0$  

Multiple Choice

The slope is...

• positive

• negative

• zero

• undefined

Multiple Choice

The trend is...

• increasing

• decreasing

• horizontal line

• vertical line

Activity #2.

In your paper, graph the following linear equations and observe the slope and the trend.

•  $y=-5x-2$  

•  $2x+3y=6$  

•  $-x-y+7=0$  

Multiple Choice

The slope is...

• undefined

• zero

• negative

• positve

Multiple Choice

The trend is...

• increasing

• decreasing

• horizontal line

• vertical line

Activity #3.

In your paper, graph the following linear equations and observe the slope and the trend.

•  $y=2$  

•  $y=-7$  

•  $y+\frac{1}{3}=0$  

Multiple Choice

The slope is...

• negative

• undefined

• positive

• zero

Multiple Choice

The trend is...

• increasing

• decreasing

• vertical line

• horizontal line

Activity #4.

In your paper, graph the following linear equations and observe the slope and the trend.

•  $x=5$  

•  $x=-7$  

•  $x-\frac{1}{8}=0$  

Multiple Choice

The slope is...

• negative

• undefined

• positive

• zero

Multiple Choice

The trend is...

• increasing

• decreasing

• vertical line

• horizontal line

Note:

• the line is described as increasing if it points upward to the right

• the line is decreasing if it points downward to the right

Note:

The trend actually depends on how the variable y behaves as the variable x increases.

- For increasing line, the variable y increases as the x increases.

- For decreasing line, the variable y decreases as the variable x increases.

The variable x is often called the independent variable, and the variable y is the dependent variable.

Intercepts

Intercepts are also properties if the graph of a linear equation that can describe its behavior.

Note that:

It should be clear from the plot above what it means for the slope of a line to be positive. As one moves to the right along the x-axis, the values of the y-coordinate of points on the line are also increasing.

When taken as trend lines, it is sometimes said that in these cases, "the y variable is positively correlated with the x variable."

end

Please don't forget to answer the Guide Questions in the Let Us Connect channel.