Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

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1:42 minutes

Problem 31

Textbook Question

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)

Verified step by step guidance

Identify the given information: The slope of the line is 0, and the y-intercept is \( \left(0, \frac{3}{2}\right) \).

Recall that a line with a slope of 0 is a horizontal line.

The equation of a horizontal line is of the form \( y = b \), where \( b \) is the y-coordinate of the y-intercept.

Substitute the y-intercept value into the equation: \( y = \frac{3}{2} \).

Since the problem asks for the equation in slope-intercept form, the equation \( y = \frac{3}{2} \) is already in the correct form.

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Key Concepts

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

Slope

Slope is a measure of the steepness or incline of a line, typically represented as 'm' in the slope-intercept form of a linear equation, y = mx + b. A slope of 0 indicates a horizontal line, meaning there is no change in the y-value as the x-value changes. This is crucial for understanding how the line behaves in relation to the x-axis.

Y-Intercept

The y-intercept is the point where a line crosses the y-axis, represented as (0, b) in the slope-intercept form y = mx + b. In this case, the y-intercept is given as (0, 3/2), indicating that when x = 0, y equals 3/2. This point is essential for graphing the line and understanding its position on the coordinate plane.

Standard Form of a Linear Equation

The standard form of a linear equation is typically expressed as Ax + By = C, where A, B, and C are integers, and A should be non-negative. This form is useful for quickly identifying intercepts and is often used in conjunction with slope-intercept form to convert between different representations of a line. Understanding how to manipulate these forms is key to solving linear equations.