The Slope of a Line. Finding the Change with Growth Triangles What is the growth factor for this line? 1 1 1 9 9 9 Change in y direction Change in x direction.

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Presentation transcript:

The Slope of a Line

Finding the Change with Growth Triangles What is the growth factor for this line? Change in y direction Change in x direction

Slope of a Line The slope is a measure of steepness. It is the ratio of the vertical change to the horizontal change OR the ratio of the change in y to the corresponding change in x. “Delta y” = Change in y “Delta x” = Change in x Example: What is the slope of the line? = 4 = 2 What is the equation of the line? Slope Triangle

Slope-Intercept Form First plot the y-intercept on the y-axis Next, use rise over run to plot new points Now connect the points with a line! You can go backwards if you need! Graph:

Steepness of a Line What makes a line steeper? The slope is further away from 0. The slope is closer to 0. What makes a line less steep?

Different Values of Slope NegativeZeroPositive DecreasingHorizontalIncreasing Negative Positive Zero Positive Always “run” to the right

Parallel Lines The slopes of parallel lines are Example: equal.... The rate of change of parallel lines is the same. NOTE: The parallel lines can NOT have the same y-intercept. Or else they would intersect all of the time since they would be the same line.

Vertical Lines The slope of a vertical line isundefined. Example: Find the slope of the line below.... The graph is not changing in the x-direction You can not divide by 0.

Slope Formula The slope of the line through the points (x 1, y 1 ) and (x 2, y 2 ) is given by: Ex: Find the slope between (2, -14) and (10,30)