Domanda del libro di testo
Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x) = √(x+1)-1
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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 79
Find the value of y if the line through the two given points is to have the indicated slope. (3, y) and (1, 4), m = −3
Guida verificata passo dopo passo1
Recall the formula for the slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[m = \frac{y_2 - y_1}{x_2 - x_1}\]
Identify the given points and slope:
Point 1: \((3, y)\), Point 2: \((1, 4)\), and slope \(m = -3\).
Substitute the known values into the slope formula:
\[-3 = \frac{4 - y}{1 - 3}\]
Simplify the denominator:
\[-3 = \frac{4 - y}{-2}\]
Solve the equation for \(y\) by multiplying both sides by \(-2\) and then isolating \(y\).
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Slope of a Line
The slope of a line measures its steepness and is calculated as the ratio of the change in y-values to the change in x-values between two points. It is given by m = (y2 - y1) / (x2 - x1). Understanding slope is essential to relate the points and the given slope.
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The Slope of a Line
Using Coordinates to Find Unknown Values
When one coordinate is unknown, you can use the slope formula and the known slope to set up an equation. By substituting the known values and solving for the unknown coordinate, you find the missing value that satisfies the slope condition.
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05:10Graphs & the Rectangular Coordinate System
Solving Linear Equations
After substituting values into the slope formula, you get a linear equation in terms of the unknown variable. Solving this equation involves basic algebraic manipulation such as addition, subtraction, multiplication, or division to isolate and find the unknown.
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04:02Solving Linear Equations with Fractions
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