Problem 1
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. $$(4,7)\( and \)(8,10)$$
Step-by-Step Solution
Verified Answer
The slope of the line passing through the points (4,7) and (8,10) is 3/4. The line rises.
1Step 1: Identify the Coordinates
The coordinates given in the problem are (4,7) and (8,10). We can let (4,7) be \((x1, y1)\) and (8,10) be \((x2, y2)\).
2Step 2: Apply the Slope Formula
Now we can substitute these coordinates into the slope formula, which is \((y2 - y1) / (x2 - x1)\). This gives us: \((10 - 7) / (8 - 4)\) = 3 / 4.
3Step 3: Find the Description of the Line
Since 3 / 4 is a positive number, it can be inferred that the line rises. Also, it's not 0, so we know the line isn't horizontal. And since it's defined (we can calculate it without getting an error), it's not a vertical line.
Other exercises in this chapter
Problem 1
Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ g(x)=x^{2}-2 $$
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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)=4 x \text { and } g(x)=\frac{x}
View solution Problem 1
If \(f(x)=2 x^{2}-5\) and \(g(x)=3 x+7,\) find: a. \((f+g)(x)\) b. \((f+g)(4)\)
View solution Problem 1
In Exercises \(1-8,\) determine whether each relation is a function. Give the domain and range for each relation. $$\\{(1,2),(3,4),(5,5)\\}$$
View solution