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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
Chapter 3, Problem 4

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

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1
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.
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Slope-Intercept Form

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.
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Graphing Intercepts

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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