Answer:
Constant of variation: 1/4
Slope of the line: 1/4
Step-by-step explanation:
The constant of variation means the relationship between variables does not change. When we want to identify the constant of variation for an equation, it is helpful to refer to one of the following formulas: xy = k (inverse variation) or y/x = k (direct variation), where k is the constant of variation.
The slope formula states that m = (y2 -- y1) / (x2 -- x1). The slope formula can be read as "slope equals the second y coordinate minus the first y-coordinate over the second x-coordinate minus the first x-coordinate".
Answer:
Step-by-step explanation:
Given:
Length of rectangular garden = (x + 2) ft
Width = (x + 7) ft
Required:
a. Polynomial expression of the area of the garden
b. Polynomial expression of the perimeter of the garden
SOLUTION:
Area of the rectangular garden = length × width
Expand using the distributive property of multiplication
Perimeter = 2(length) + 2(width)
Collect like terms
In a function, each input (x-) value has exactly one output (y-) value. That's not the case here, where we have (-4,5) and (-4,3) (two different y-values for one x-value). Eliminating either (-4,5) or (-4,3) will make this relation into a function.
Answer: Graph D (bottom right corner)
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Explanation:
The equation y = 3x+3 is in slope intercept form y = mx+b
m = 3 = slope
b = 3 = y intercept
In this case, both the slope and y intercept are the same (though in general they tend not to be).
The positive slope value means the line goes uphill as you move from left to right. The positive y intercept means the diagonal line crosses the y axis somewhere above the horizontal x axis. Specifically, it crosses the y axis at y = 3
Graph D is the only graph that has such a line on it. Graphs A, B and C have the positive slope line where they have a negative y intercept, so we can rule them out.
You can use graphing tools such as Desmos or Geogebra to help confirm this answer. You could also make a table of values, and plot each point, to form the lines. Two points is the minimum amount needed to form any line.
To solve for x in terms of b, simply treat b as a number, and solve for x as usual: first of all, we expand the left hand side:
Subtract 10 from both sides:
Divide both sides by -2b:
This means that in particular, if we set 
, we have
