Domanda del libro di testo
Graph both equations in the same rectangular coordinate system and find all points of intersection. Then show that these ordered pairs satisfy the equations. x² + y² = 16, x-y = 4
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 3, Problema 66a
In Exercises 59-66, a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. 4y+ 28 = 0
Guida verificata passo dopo passo1
Rewrite the given equation in slope-intercept form (y = mx + b). Start by isolating the term with 'y' on one side of the equation. Subtract 28 from both sides to get 4y = -28.
Divide both sides of the equation by 4 to solve for 'y'. This simplifies to y = -7.
Identify the slope (m) and y-intercept (b) from the slope-intercept form y = mx + b. In this case, the slope (m) is 0 (since there is no x-term), and the y-intercept (b) is -7.
To graph the linear function, plot the y-intercept (0, -7) on the coordinate plane. Since the slope is 0, the line is horizontal, meaning it does not rise or fall as x changes.
Draw a horizontal line through the point (0, -7) to complete the graph of the linear function.
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Slope-Intercept Form
The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. This form is particularly useful for quickly identifying the slope and y-intercept of a line, which are essential for graphing linear functions.
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03:56
Slope-Intercept Form
Slope
The slope of a line measures its steepness and direction, calculated as the change in y over the change in x (rise over run). A positive slope indicates the line rises from left to right, while a negative slope indicates it falls. Understanding slope is crucial for interpreting the relationship between variables in a linear equation.
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05:17Types of Slope
Y-Intercept
The y-intercept is the point where a line crosses the y-axis, represented by the value of y when x is zero. In the slope-intercept form, this value is denoted by b. Identifying the y-intercept is important for graphing linear equations, as it provides a starting point on the graph.
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04:08Graphing Intercepts
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