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Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 2 - Functions and GraphsProblem 43
Chapter 3, Problem 43

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (4, -7) and parallel to the line whose equation is 3x + y - 9 = 0.

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Rewrite the given line equation 3x + y - 9 = 0 in slope-intercept form (y = mx + b) by isolating y. Subtract 3x and add 9 to both sides to get y = -3x + 9. Here, the slope (m) of the given line is -3.
Since the new line is parallel to the given line, it will have the same slope. Therefore, the slope of the new line is also m = -3.
Use the point-slope form of a line equation, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. Substitute the point (4, -7) and the slope m = -3 into the formula: y - (-7) = -3(x - 4).
Simplify the point-slope form equation: y + 7 = -3(x - 4). Expand the right-hand side to get y + 7 = -3x + 12.
Convert the equation into slope-intercept form (y = mx + b) by isolating y. Subtract 7 from both sides to get y = -3x + 5. The final equations are: Point-slope form: y + 7 = -3(x - 4), and Slope-intercept form: y = -3x + 5.

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Key Concepts

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

Point-Slope Form

Point-slope form is a way to express the equation of a line given a point on the line and its slope. The formula is written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly useful for quickly writing the equation of a line when you know a specific point and the slope.
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Point-Slope Form

Slope-Intercept Form

Slope-intercept form is another way to express the equation of a line, defined as y = mx + b, where m is the slope and b is the y-intercept. This form allows for easy identification of the slope and where the line crosses the y-axis. Converting from point-slope to slope-intercept form is a common task in algebra.
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Parallel Lines

Parallel lines are lines in a plane that never intersect and have the same slope. When writing the equation of a line parallel to another, it is essential to use the same slope as the given line. In this case, the slope can be derived from the standard form of the line's equation, allowing for the creation of a new line that maintains the same direction.
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Related Practice
Textbook Question

Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. (x − 3)² + (y + 1)² = 36

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Textbook Question

Give the slope and y-intercept of each line whose equation is given. Then graph the linear function. f(x) = (3/4)x-2

Textbook Question

Find f+gf+g, f−gf-g, fgfg, and fg\(\frac{f}{g}\). Determine the domain for each function.

f(x)=6−1xf\(\left\)(x\(\right\))=6-\(\frac{1}{x}\), g(x)=1xg\(\left\)(x\(\right\))=\(\frac{1}{x}\)

Textbook Question

In Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = (x − 1)², x ≤ 1

Textbook Question

Use the graph of y = f(x) to graph each function g. g(x) = (1/2)f(2x)

Textbook Question

Find ƒ+g and determine the domain for each function.

f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)