What do the following two equations represent? • y-8=1/5(x+5) • y-8=-1/2(x+5)
1 answer:
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Answer:
Both functions have negative rates of change
Function B has a greater rate of change than Function A
Step-by-step explanation:
we know that
<em>Function A</em>
The rule for Function A is
This is the equation of a proportional relationship (the line passes through the origin)
The slope is equal to
<em>Function B</em>
Find the equation of the function B
we have the points (-2,0) and (0,-2)
<em>Find the slope</em>
The formula to calculate the slope between two points is equal to
substitute the values
The equation of the function B in slope intercept form is equal to
we have
substitute
<u><em>Verify each statement</em></u>
Option 1) Both functions have negative rates of change
The statement is true
Because, the rate of change is the slope of the linear equation
Function A ---->
Function B ---->
Option 2) Both functions have the same rate of change.
The statement is false (see the explanation)
The rate of change are different ( m=-2/3 and m=-1)
Option 3) When graphed, Function A and Function B are parallel
The statement is false
When graphed, Function A and Function B are intersecting lines, because their slopes are different
Option 4) Function B has a greater rate of change than Function A
The statement is true
Remember that the rate of change can be either positive (increasing function) or negative (decreasing function). To find out which function has a greater rate of change, compare the absolute value of their slopes
therefore
1 > 2/3