Solve the logarithmic equation. Round to the nearest ten-thousandth if necessary. log(x+9)-log x=3
1 answer:
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Answer:
Part 1) The y-intercept is the point (0,-3)
Part 2) The slope in fraction form is
Part 3) The graph in the attached figure
Step-by-step explanation:
we have
Part 1) What is the y-intercept?
Remember that
The y-intercept is the value of y when the value of x is equal to zero
so
For x=0
substitute in the linear equation and solve for y
The y-intercept is the point (0,-3)
Part 2) What is the slope (in fraction form)?
we have
This is the equation of the line in slope intercept form
where
m is the slope or unit rate
b is the y-intercept
so
In fraction form is
The slope is negative, that means, is a decreasing function (as the x-values increases the y-values decreases)
Part 3) Graph the line
To graph the line we need two points
From the y-intercept (0,-3) use the slope to find your next point
The slope is -2, so you will rise -2 (2 units down) and run 1 (1 unit to the right).
The next point is (0+1,-3-2) -----> (1,-5)
so
Plot the points (0,-3) and (1,-5), connect them and graph the line
The graph in the attached figure
