Problem 74
Question
Find the slope of the line passing through each pair of points or state that the slope is undefined. Assume that all variables represent positive real numbers. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(-a, 0) \text { and }(0,-b)$$
Step-by-Step Solution
Verified Answer
The slope of the line passing through the points (-a, 0) and (0,-b) is -b/a, and the line falls.
1Step 1: Understand the Slope Formula
The slope of the line passing through the points \((x_1,y_1)\) and \((x_2,y_2)\) is given by \(m = (y_2 - y_1) / (x_2 - x_1)\).
2Step 2: Substitute the Coordinates into the Formula
Substitute \((x_1,y_1) = (-a, 0)\) and \((x_2,y_2) = (0,-b)\) into the formula, to get \(m = (-b - 0) / (0 - (-a)) = -b / a\).
3Step 3: Analyze The Slope
The slope \(m = -b / a\) is negative, so the line falls. Because \(a\) and \(b\) represent positive real numbers, the slope will always be a negative number when dividing a positive number by another positive number.
Other exercises in this chapter
Problem 74
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find and simplify the difference quotient $$ \frac{f(x+h)-f(x)}{h}, h \neq 0 $$ for the given function. $$ f(x)=\sqrt{x} $$
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