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Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경
3장, 문제 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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.
추천 영상:
03:56
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.
추천 영상:
04:08
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.
추천 영상:
5:14
Evaluate Logarithms