Help please!!!! It’s on illustrative mathematics and I need help!!
Answer:
See attached
Step-by-step explanation:
You want the slopes of the various graphs, and a description of how you got it.
Slope
As you know from your real-world experience a steep slope has more vertical change in the same horizontal distance than one that is less steep. When the height increases over a horizontal distance, we say the slope is positive. When the height decreases, the slope is negative.
In the real world, a downhill (negative) slope turns into a positive (uphill) slope if you just turn around and go the other direction.
On an x-y (Cartesian) coordinate plane, we define the direction as positive to the right. So, a line or curve with positive slope goes up to the right. A line or curve with negative slope goes down to the right. (The slope of a horizontal line is zero. The slope of a vertical line is "undefined.")
Measure of slope
Slope can be described different ways. The natural slope of a pile of loose material (sand, gravel, rock, salt, coal, and the like) can be described by its angle of repose. Dry sand may have an angle of repose of as much as 34°. When it is filled with water, it may slump to 15° or so.
The slope, or grade, of a roadway or other path is often described as a percentage (feet of rise or drop per 100 horizontal feet). Many places a 10% grade (about 5.7°) would be considered a pretty steep slope. The steepest hills in San Francisco have a 31.5% grade. A "black diamond" ski run is one with a slope of 40% (about 22°) or more.
In Algebra, we usually give a slope a numerical value. Its units will be the ratio of the units of the vertical measure on a graph to the units of the horizontal measure on the graph. For a graph with no particular units, or where the horizontal and vertical units are the same, the slope is simply a "pure number" that has no units.
Calculating slope
Slope is defined as the ratio of vertical change to the corresponding horizontal change. On a graph, the vertical change between two points is the difference of their vertical (y) coordinates. The horizontal change is the difference of the horizontal (x) coordinates taken in the same order.
The formula for the slope between two points (x₁, y₁) and (x₂, y₂) is ...
[tex]\text{slope}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The points can be designated as "point 1" and "point 2" in any order, but the chosen designation needs to be used consistently in the calculation.
If the denominator is zero, the slope is "undefined."
1. Given graphs
The graphs show the coordinates of the points you are to use to calculate the slope. In the attachment, we use the point on the right as "point 2" and the point on the left as "point 1". That makes the difference of x-coordinates positive, so the sign of the slope will be the sign of the difference of corresponding y-coordinates. (The slope is positive in all cases here.)
2. Procedure
The "procedure" is simply a description of what you did to find the slope. It is described above, and also in the attachment. You know what you did, so all you need to do is write that down.
3. Expression
The answer to question 3 is the same as the answer to any of the parts of question 1, except you're using different symbols for the coordinates of the point. Considering graph A, you're using "u" and "v" instead of "4" and "9". The letters go in the same places the numbers do in the equation for slope.
The attachment has the answers to the questions.
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