Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 4

Chapter 3, Problem 4

Fill in the blank to correctly complete each sentence. The y-intercept of the graph of y = -2x + 6 is ________.

Verified step by step guidance

Recall that the y-intercept of a linear equation in the form $y = mx + b$ is the value of $y$ when $x = 0$.

Identify the equation given: $y = -2x + 6$.

Substitute $x = 0$ into the equation to find the y-intercept: $y = -2(0) + 6$.

Simplify the expression: $y = 0 + 6$.

Conclude that the y-intercept is the point where $y = 6$, or the coordinate $(0, 6)$.

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Key Concepts

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

Slope-Intercept Form of a Linear Equation

The slope-intercept form is written as y = mx + b, where m represents the slope and b represents the y-intercept. This form makes it easy to identify the y-intercept directly from the equation.

Y-Intercept

The y-intercept is the point where the graph crosses the y-axis, which occurs when x = 0. In the equation y = mx + b, the y-intercept is the constant term b.

Evaluating the Equation at x = 0

To find the y-intercept, substitute x = 0 into the equation and solve for y. This gives the exact value of the y-intercept, confirming the constant term in the slope-intercept form.

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Related Practice

Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. $ƒ (x) = x + 1$ and $g (x) = x^{2}$

$open paren f with hook slash g close paren times 2$

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Textbook Question

Fill in the blank(s) to correctly complete each sentence. For the function ƒ(x) = -4x + 2, ƒ(-2)= ______.

Textbook Question

Fill in the blank to correctly complete each sentence. The x-intercept of the graph of 2x + 5y = 10 is ________.

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The equation y = 4x - 6 defines a function with independent variable______ and dependent variable ________ .

Textbook Question

Without using paper and pencil, evaluate each expression given the following functions. $ƒ (x) = x + 1$ and $g (x) = x^{2}$

$open paren f with hook composed with g close paren times 2$

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Textbook Question

To answer each question, refer to the following basic graphs. Which one is the graph of ƒ(x)=x³? What is its range?

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