Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 45

Chapter 3, Problem 45

Find the slope of the line satisfying the given conditions. through (5, 9) and (-2, 9)

Verified step by step guidance

Identify the coordinates of the two points given: $ (5, 9) $ and $ (-2, 9) $.

Recall the formula for the slope $ m $ of a line passing through two points $ (x_1, y_1) $ and $ (x_2, y_2) $: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substitute the given points into the slope formula: \[ m = \frac{9 - 9}{-2 - 5} \]

Simplify the numerator and denominator separately: Numerator: $ 9 - 9 = 0 $ Denominator: $ -2 - 5 = -7 $

Calculate the slope by dividing the simplified numerator by the denominator: \[ m = \frac{0}{-7} \] which simplifies to the slope value.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Slope of a Line

The slope of a line measures its steepness and direction, calculated as the ratio of the change in y-values to the change in x-values between two points. It is often represented as 'm' and found using the formula m = (y2 - y1) / (x2 - x1).

Coordinate Points

Coordinate points are pairs of numbers (x, y) that represent locations on the Cartesian plane. Understanding how to use these points is essential for calculating the slope, as the difference between their x and y values determines the line's rise over run.

Horizontal Lines

A horizontal line has a constant y-value for all points, meaning its slope is zero. Recognizing when two points share the same y-coordinate helps quickly identify that the line is horizontal and the slope is zero without further calculation.

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The Slope of a Line

Related Practice

Textbook Question

Without graphing, determine whether each equation has a graph that is symmetric with respect to the x-axis, the y-axis, the origin, or none of these. See Examples 3 and 4. y=x²+5

Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h.See Example 4.

$ƒ (x) = 4 x + 11$

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. y=√(7-2x)

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Textbook Question

Find the value of the function for the given value of x. ƒ(x)=-[[-x]], for x=2.5

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Textbook Question

For each function, find (a)ƒ(x+h), (b)ƒ(x+h)-ƒ(x), and (c)[ƒ(x+h)-ƒ(x)]/h. ƒ(x)=6x+2

Textbook Question

Find the value of the function for the given value of x. ƒ(x)=2-[[-x]], for x=3.7

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