Table of contents

0. Review of Algebra4h 18m

Algebraic Expressions
36m

Exponents
32m

Polynomials Intro
19m

Multiplying Polynomials
36m

Factoring Polynomials
1h 2m

Radical Expressions
15m

Simplifying Radical Expressions
35m

Rationalize Denominator
15m

Rational Exponents
4m

1. Equations & Inequalities3h 18m

Linear Equations
31m

Rational Equations
21m

The Imaginary Unit
6m

Powers of i
11m

Complex Numbers
36m

Intro to Quadratic Equations
18m

The Square Root Property
11m

Completing the Square
12m

The Quadratic Formula
18m

Choosing a Method to Solve Quadratics
9m

Linear Inequalities
20m

2. Graphs of Equations1h 43m

Graphs and Coordinates
7m

Two-Variable Equations
23m

Lines
1h 12m

3. Functions2h 17m

Intro to Functions & Their Graphs
35m

Common Functions
5m

Transformations
45m

Function Operations
21m

Function Composition
29m

4. Polynomial Functions1h 44m

Quadratic Functions
39m

Understanding Polynomial Functions
34m

Graphing Polynomial Functions
30m

Dividing Polynomials

Zeros of Polynomial Functions

5. Rational Functions1h 23m

Introduction to Rational Functions
9m

Asymptotes
35m

Graphing Rational Functions
38m

6. Exponential & Logarithmic Functions2h 28m

Introduction to Exponential Functions
9m

Graphing Exponential Functions
25m

The Number e
8m

Introduction to Logarithms
22m

Graphing Logarithmic Functions
18m

Properties of Logarithms
27m

Solving Exponential and Logarithmic Equations
35m

7. Systems of Equations & Matrices4h 5m

Two Variable Systems of Linear Equations
1h 7m

Introduction to Matrices
1h 11m

Determinants and Cramer's Rule
1h 3m

Graphing Systems of Inequalities
42m

8. Conic Sections2h 23m

Introduction to Conic Sections
5m

Circles
15m

Ellipses: Standard Form
33m

Parabolas
36m

Hyperbolas at the Origin
40m

Hyperbolas NOT at the Origin
12m

9. Sequences, Series, & Induction1h 22m

Sequences
40m

Arithmetic Sequences
25m

Geometric Sequences
15m

10. Combinatorics & Probability1h 45m

Factorials
11m

Combinatorics
46m

Probability
47m

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

Previous problemNext problem

2:02 minutes

Problem 39

Textbook Question

Find the slope and y-intercept of each line, and graph it. 4y = -3x

Verified step by step guidance

Step 1: The first step is to rewrite the equation in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, divide every term in the equation by 4 to isolate y. The equation becomes y = -3/4x + 0.

Step 2: Now that the equation is in slope-intercept form, we can identify the slope and the y-intercept. The slope (m) is the coefficient of x, which is -3/4. This means that for every 1 unit increase in x, y decreases by 3/4 units.

Step 3: The y-intercept (b) is the constant term, which is 0 in this case. This means that the line crosses the y-axis at the point (0,0).

Step 4: To graph the line, start by plotting the y-intercept on the y-axis. Since the y-intercept is 0, put a point at the origin (0,0).

Step 5: From the y-intercept, use the slope to find the next point. Since the slope is -3/4, go down 3 units and to the right 4 units from the y-intercept and put another point. Draw a line through these two points to complete the graph.

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Key Concepts

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

Slope

The slope of a line measures its steepness and direction, represented as 'm' in the slope-intercept form of a linear equation, y = mx + b. It is calculated as the ratio of the change in y to the change in x (rise over run). A positive slope indicates the line rises from left to right, while a negative slope indicates it falls.

Y-Intercept

The y-intercept is the point where a line crosses the y-axis, represented as 'b' in the slope-intercept form of a linear equation. It can be found by setting x to zero in the equation of the line. This value is crucial for graphing the line, as it provides a starting point on the y-axis.

Graphing Linear Equations

Graphing linear equations involves plotting points that satisfy the equation on a coordinate plane. Once the slope and y-intercept are determined, the line can be drawn by starting at the y-intercept and using the slope to find additional points. This visual representation helps in understanding the relationship between the variables in the equation.