Write an equation for each line described. Give answers in standard form for Exercises 11–20 and in slope-intercept form (if possible) for Exercises 21–32. slope 0, y-intercept (0, 3/2)

검증된 단계별 안내

Identify the slope and y-intercept given in the problem. Here, the slope is 0, and the y-intercept is the point \( (0, \frac{3}{2}) \).

Recall that a slope of 0 means the line is horizontal. A horizontal line has the form \( y = b \), where \( b \) is the y-intercept.

Since the y-intercept is \( \frac{3}{2} \), the equation of the line in slope-intercept form is \( y = \frac{3}{2} \).

To write the equation in standard form, recall that standard form is \( Ax + By = C \), where \( A, B, \) and \( C \) are integers and \( A \geq 0 \).

Rewrite \( y = \frac{3}{2} \) as \( 0 \cdot x + y = \frac{3}{2} \), or simply \( y = \frac{3}{2} \), which is already in standard form with \( A=0, B=1, C=\frac{3}{2} \). If desired, multiply through by 2 to clear the fraction: \( 0 \cdot x + 2y = 3 \).

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주요 개념

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

Slope of a Line

The slope measures the steepness of a line and is defined as the ratio of the vertical change to the horizontal change between two points. A slope of 0 means the line is horizontal, indicating no vertical change as you move along the line.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, represented as (0, b). It indicates the value of y when x is zero and is essential for writing the equation of a line.

Forms of Linear Equations

Linear equations can be expressed in various forms, including standard form (Ax + By = C) and slope-intercept form (y = mx + b). The slope-intercept form explicitly shows the slope and y-intercept, while the standard form is a rearranged version often used for certain types of problems.