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Understanding Slope: Calculations and Applications in Graphing Lines

This lesson covers the concept of slope, its significance in the context of linear equations, and how to calculate it using both points and graphs. We will explore examples, including finding the slope from given points and understanding the meaning of slope in real-world scenarios, such as road gradients. Additionally, we will discuss the differences between positive, negative, horizontal, and vertical slopes. Exercises will include tasks on finding slopes and graphing lines based on slope information, enhancing your understanding through practical applications.

leandra-knapp
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Understanding Slope: Calculations and Applications in Graphing Lines

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  1. Warm Up Given h(x) = find the following: h(-8) What value of x would make h(x) = 7? What value of x would make h(x) = -3?

  2. HW Check – 4.1

  3. Slope of a line

  4. What is the meaning of this sign? • Icy Road Ahead • Steep Road Ahead • Curvy Road Ahead • Trucks Entering Highway Ahead

  5. 100 feet 7 feet 7% What does the 7% mean? 7% is the slope of the road. It means the road rises 7 feet vertically for every 100 feet horizontally. So, what is the meaning of slope??? Slope is the steepness of a line.

  6. 1) Determine the slope (rate of Change) of the line. When given the graph, it is easier to apply “rise over run”. Rise – is the vertical change. Run – is the horizontal change.

  7. Find the slope: 2) 3)

  8. Slope can be expressed different ways: ****Slope is the same as rate of change**** A line has a positive slope if it is going uphill from left to right. A line has a negative slope if it is going downhill from left to right.

  9. 2) Find the slope (rate of change) of the line that passes through the points (-2, -2) and (4, 1). When given points, it is easier to use the formula!

  10. Find the slope (rate of change) of the line that passes through (3, 5) and (-1, 4).

  11. You try! • Find the slope of the line that goes through the points (-5, 3) and (2, 1).

  12. What is the slope of a horizontal line? H0y The line doesn’t rise! All horizontal lines have a slope of 0.

  13. What is the slope of a vertical line? VuX The line doesn’t run! All vertical lines have an undefined slope.

  14. VuXand H0y VuX: Vertical lines have undefined slope with an equation x = a number. HOy: Horizontal lines have zero as their slope with an equation y = a number.

  15. Draw a line through the point (2,0) that has a slope of 3. 1. Graph the ordered pair (2, 0). 2. From (2, 0), apply rise over run (write 3 as a fraction). 3. Plot a point at this location. 4. Draw a straight line through the points.

  16. Homework: 4.2 Quiz Friday!

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