Problem 9
Question
Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(5,3)\( and \)(5,-2)$$
Step-by-Step Solution
Verified Answer
The slope of the line passing through the points (5,3) and (5,-2) is undefined, indicating a vertical line.
1Step 1: Identify the given points
The points given are (5,3) and (5,-2). For easier identification, let's call (5,3) as point 1 and represented by \(x1,y1\) and (5,-2) as point 2 and represented by \(x2, y2\).
2Step 2: Insert the values into the slope formula
We can apply the slope formula, \(m = \frac{y2 - y1}{x2 - x1}\). Replacing with our points we have: \(m = \frac{-2 - 3}{5 - 5}\)
3Step 3: Calculate the Slope
Solving the equation we get \(m = \frac{-5}{0}\). But any number divided by zero is undefined.
4Step 4: Identify the type of line
Since the slope is undefined, the line through the points is vertical.
Other exercises in this chapter
Problem 8
Find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (-4,-1) \text { and }(2,-3) $$
View solution Problem 9
Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=2(x-2)^{2} $$
View solution Problem 9
Find \(f+g, f-g, f g,\) and \(\frac{f}{g}\). Determine the domain for each function. $$f(x)=2 x^{2}-x-3, g(x)=x+1$$
View solution Problem 9
Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=-x \text { and } g(x)=-x$$
View solution