Answer:
Rate of change for the linear relationship modeled is
Step-by-step explanation:
As the there is a linear relationship in the points, so all these points will be on a single straight line. Hence the slope will be same throughout all the points.
We know that, the slope of the line joining (x₁, y₁) and (x₂, y₂) is,
Putting the points as (-1, 10) and (1, 9), we get
Rate of change is the slope of the line joining all these points.
The problem asks for a location that is equidistant from towns A and B and lies on the given road. Calculating the midpoint of A and B, we get (5, 1.5). However, this point does not lie on the road denoted by -x + 7y = -4. So, we cannot determine the exact location of the school with the given conditions.
In this problem, the location of the school should be the midpoint of the line between towns A and B as it is equidistant from both towns. First, let's calculate the midpoint (M) coordinates. The formulas for finding the x and y coordinates of the midpoint are (x1 + x2) / 2 and (y1 + y2) / 2 respectively. Using these formulas, we get the coordinates of M as (2+8)/2, (-2+5)/2 = (5, 1.5). However, we should ensure that this point lies on the given road, which is denoted by the equation -x + 7y = -4. Substituting the coordinates of M in the equation, we get -5 + 7*1.5 = -5 + 10.5 = 5.5 which is not equal to -4. So, (5, 1.5) is not a valid location for the school. Unfortunately, with the given conditions, we cannot determine the exact location of the school. Additional information or revision of the conditions might be necessary to solve this problem.
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y = (-1/15x) - 8
y = -9x - 7
y = (1/5x) - 3