Textbook Question
Find the domain of each function. f(x) = √(24 - 2x)
Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
Chapter 3, Problem 24
Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Slope = - 3/5, passing through (10, −4)
Verified step by step guidance1
Recall the point-slope form of a line equation: \(y - y_1 = m(x - x_1)\), where \(m\) is the slope and \((x_1, y_1)\) is a point on the line.
Substitute the given slope \(m = -\frac{3}{5}\) and the point \((10, -4)\) into the point-slope form: \(y - (-4) = -\frac{3}{5}(x - 10)\).
Simplify the left side by changing \(y - (-4)\) to \(y + 4\), so the equation becomes \(y + 4 = -\frac{3}{5}(x - 10)\).
To write the equation in slope-intercept form \(y = mx + b\), distribute the slope on the right side: \(y + 4 = -\frac{3}{5}x + \frac{3}{5} \times 10\).
Finally, isolate \(y\) by subtracting 4 from both sides: \(y = -\frac{3}{5}x + \frac{3}{5} \times 10 - 4\).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Point-Slope Form of a Line
The point-slope form is an equation of a line expressed as y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. It directly uses the given slope and point to write the line's equation.
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Point-Slope Form
Slope-Intercept Form of a Line
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. After finding the equation in point-slope form, you can solve for y to rewrite it in slope-intercept form, identifying the y-intercept.
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02:35Graphing Lines in Slope-Intercept Form
Slope of a Line
Slope measures the steepness of a line and is the ratio of vertical change to horizontal change between two points. A slope of -3/5 means the line falls 3 units vertically for every 5 units it moves horizontally to the right.
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Related Practice
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