Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 20

Chapter 3, Problem 20

Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−2, 6) and is perpendicular to the line whose equation is x = -4.

Verified step by step guidance

Identify the given information: the function ƒ passes through the point $(-2, 6)$ and is perpendicular to the line $x = -4$.

Recall that the line $x = -4$ is a vertical line, which means its slope is undefined.

Since the line we want is perpendicular to a vertical line, it must be a horizontal line. Horizontal lines have a slope of 0.

Use the slope-intercept form of a line, which is $y = m x + b$, where $m$ is the slope and $b$ is the y-intercept. Here, $m = 0$, so the equation simplifies to $y = b$.

Substitute the point $(-2, 6)$ into the equation $y = b$ to find $b$: since $y = 6$, the equation of the line is $y = 6$.

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Key Concepts

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

Slope-Intercept Form

The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b is the y-intercept. This form makes it easy to identify the slope and where the line crosses the y-axis, which is essential for graphing and writing linear equations.

Perpendicular Lines

Two lines are perpendicular if their slopes are negative reciprocals of each other. For vertical and horizontal lines, a vertical line has an undefined slope, and a line perpendicular to it is horizontal with a slope of zero. Understanding this helps determine the slope of the required line.

Using a Point to Find the Equation

Given a point on the line and the slope, you can substitute these values into the slope-intercept form to solve for the y-intercept b. This step is crucial to write the complete equation of the line that meets the given conditions.

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Textbook Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = −1, passing through (−4, − 1/4)

Textbook Question

Write an equation in slope-intercept form of a linear function f whose graph satisfies the given conditions. The graph of ƒ passes through (−1, 5) and is perpendicular to the line whose equation is x = 6.

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Use the graph of y = f(x) to graph each function g. g(x) = f(x+1)

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Determine whether each equation defines y as a function of x. $y = - \sqrt{x + 4}$

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Textbook Question

Determine whether each equation defines y as a function of x. y = √x +4

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Find the domain of each function. f(x) = √(5x+35)