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

2:22 minutes

Problem 1

Textbook Question

Write an equation for line L in point-slope form and slope-intercept form.

Verified step by step guidance

Identify the slope of the given line y = 3x + 2. Since the equation is in slope-intercept form y = mx + b, the slope m is 3.

Since line L is parallel to y = 3x + 2, it has the same slope. So, the slope of line L is also 3.

Use the point-slope form of a line equation, which is \(y - y_1 = m(x - x_1)\), where \((x_1, y_1)\) is a point on the line and m is the slope. Here, the point is (-1, 2) and the slope is 3.

Substitute the point (-1, 2) and slope 3 into the point-slope form: \(y - 2 = 3(x - (-1))\) or \(y - 2 = 3(x + 1)\).

To write the equation in slope-intercept form, simplify the point-slope form by distributing the slope and solving for y: \(y - 2 = 3x + 3\), then add 2 to both sides to get \(y = 3x + 5\).

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Key Concepts

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

Slope of Parallel Lines

Parallel lines have the same slope. Since line L is parallel to y = 3x + 2, it shares the slope of 3. This means the rate of change for line L is identical to the given line, which is essential for writing its equation.

Point-Slope Form of a Line

The point-slope form is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. This form is useful when you know a point on the line and its slope, allowing you to write the equation directly from given information.

Slope-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. After finding the slope and using a point to solve for b, this form provides a clear way to express the line's equation and easily graph it.

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Related Practice

Textbook Question

In Exercises 59-66, a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. 8x – 4y – 12 =0

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Textbook Question

In Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quotient from part (b) to find the remaining roots and solve the equation. 6x³+25x²−24x+5=0

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Textbook Question

Solve each system for x and y, expressing either value in terms of a or b, if necessary. Assume that a ≠ 0 and b ≠ 0. For the linear function f(x) = mx + b, f(−2) = 11 and ƒ(3) = -9. Find m and b.

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Textbook Question

Write an equation in point-slope form and slope-intercept form for the line passing through (-2, -6) and perpendicular to the line whose equation is x − 3y+ 9 = 0.

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Textbook Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (−8, −10) and parallel to the line whose equation is y = −4x + 3

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Textbook Question

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (2, −3) and perpendicular to the line whose equation is y = (1/5)x + 6

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Textbook Question

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (4, 7) and (8, 10)

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