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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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.

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."

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