Problem 7
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. $$(-2,4)\( and \)(-1,-1)$$
Step-by-Step Solution
Verified Answer
The slope of the line passing through the points (-2,4) and (-1,-1) is -5, and the line is falling.
1Step 1: Identify the given points
The two points given in the problem are (-2,4) and (-1,-1)
2Step 2: Use the slope formula
The formula for the slope (m) between any two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is defined as \(m = \frac{y_2 - y_1}{x_2 - x_1}\). This formula calculates the difference in y values divided by the difference in x values between the two points.
3Step 3: Substitute the given points into the slope formula
Plug the coordinates of the two points into the slope formula. We denote (-2, 4) as \( (x_1, y_1) \) and (-1, -1) as \( (x_2, y_2) \). This becomes \(m = \frac{-1 - 4}{-1 - (-2)}\).
4Step 4: Calculate the slope
Performing the indicated operations gives us \(m = \frac{-5}{1} = -5\)
5Step 5: Determine the direction of the line
Since the computed slope is negative, we can say the line falls.
Other exercises in this chapter
Problem 6
Find the distance between each pair of points. If necessary, round answers to two decimals places. $$ (0,0) \text { and }(3,-4) $$
View solution Problem 7
Begin by graphing the standard quadratic function, \(f(x)=x^{2} .\) Then use transformations of this graph to graph the given function. $$ h(x)=(x-2)^{2}+1 $$
View solution Problem 7
Find \(f+g, f-g, f g,\) and \(\frac{f}{g}\). Determine the domain for each function. $$f(x)=x-5, g(x)=3 x^{2}$$
View solution Problem 7
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)=\frac{3}{x-4} \text { and } g(x
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