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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 50
Chapter 3, Problem 50

Graph using intercepts: 2x - 5y - 10 = 0

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1
Rewrite the equation in standard form if necessary. The given equation is already in standard form: 2x - 5y - 10 = 0.
To find the x-intercept, set y = 0 in the equation and solve for x. Substitute y = 0 into 2x - 5y - 10 = 0, which simplifies to 2x - 10 = 0. Solve for x.
To find the y-intercept, set x = 0 in the equation and solve for y. Substitute x = 0 into 2x - 5y - 10 = 0, which simplifies to -5y - 10 = 0. Solve for y.
Plot the x-intercept and y-intercept on a coordinate plane. The x-intercept is the point where the graph crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis.
Draw a straight line through the two intercepts. This line represents the graph of the equation 2x - 5y - 10 = 0.

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Key Concepts

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

Intercepts

Intercepts are points where a graph crosses the axes. The x-intercept occurs when y = 0, and the y-intercept occurs when x = 0. Finding these points is essential for graphing linear equations, as they provide two key coordinates that define the line's position on the Cartesian plane.
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Linear Equations

A linear equation is an equation of the first degree, meaning it can be expressed in the form Ax + By + C = 0, where A, B, and C are constants. The graph of a linear equation is a straight line, and understanding its structure helps in identifying its slope and intercepts, which are crucial for graphing.
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Slope-Intercept Form

The slope-intercept form of a linear equation is given by y = mx + b, where m represents the slope and b represents the y-intercept. While the question focuses on intercepts, converting the equation to this form can provide additional insights into the line's steepness and direction, enhancing the graphing process.
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Related Practice
Textbook Question

In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)

Textbook Question

In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)

Textbook Question

In Exercises 51–54, graph the given square root functions, f and g, in the same rectangular coordinate system. Use the integer values of x given to the right of each function to obtain ordered pairs. Because only nonnegative numbers have square roots that are real numbers, be sure that each graph appears only for values of x that cause the expression under the radical sign to be greater than or equal to zero. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = √x (x = 0, 1, 4, 9) and g(x) = √x −1 (x = 0, 1, 4, 9)

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 + 1)² + y² = 25

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Textbook Question

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

Textbook Question

Find

a. (fog) (x)

b. (go f) (x)

c. (fog) (2)

d. (go f) (2).

f(x) = 2x, g(x) = x+7