Domanda del libro di testo
Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. x² + y² - 6y -7=0
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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 60
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. 4x+y-6=0
Guida verificata passo dopo passo1
Start with the given equation: \(4x + y - 6 = 0\).
Rewrite the equation to solve for \(y\) in terms of \(x\) to get it into slope-intercept form $y = mx + b$. To do this, isolate \(y\) by subtracting \$4x$ and adding \(6\) to both sides: $y = -4x + 6$.
Identify the slope \(m\) and the y-intercept \(b\) from the slope-intercept form $y = mx + b$. Here, the slope \(m\) is the coefficient of \(x\), which is \(-4\), and the y-intercept \(b\) is the constant term, which is \(6\).
To graph the linear function, start by plotting the y-intercept point \((0, 6)\) on the coordinate plane.
Use the slope \(m = -4\) to find another point. Since slope is rise over run, from the y-intercept move down 4 units (rise = -4) and right 1 unit (run = 1) to plot a second point. Then draw a straight line through these two points to complete the graph.
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Slope-Intercept Form
The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. Rewriting an equation into this form makes it easier to identify these values and to graph the line.
Video consigliato:
03:56
Slope-Intercept Form
Slope of a Line
The slope (m) measures the steepness and direction of a line, calculated as the ratio of the change in y to the change in x (rise over run). It indicates how much y changes for a unit change in x and is essential for understanding the line's behavior.
Video consigliato:
06:49The Slope of a Line
Graphing Using Slope and Y-Intercept
Graphing a linear function involves plotting the y-intercept (where the line crosses the y-axis) and then using the slope to find other points by moving vertically and horizontally. This method provides a straightforward way to visualize the line on the coordinate plane.
Video consigliato:
02:35Graphing Lines in Slope-Intercept Form
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