Table of contents

0. Review of Algebra4h 16m
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 19m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

2:16 minutes

Problem 42b

Textbook Question

Graph each equation. x - 4y = 8

Verified step by step guidance

Step 1: The given equation is in the standard form of a linear equation, which is Ax + By = C. In this case, A=1, B=-4, and C=8.

Step 2: To graph this equation, it's often easiest to first convert it to slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To do this, isolate y in the equation. You can do this by subtracting x from both sides and then dividing by -4.

Step 3: Once the equation is in slope-intercept form, identify the slope and the y-intercept. The slope is the coefficient of x, and the y-intercept is the constant term.

Step 4: Start by plotting the y-intercept on the y-axis. This is the point where the line crosses the y-axis.

Step 5: From the y-intercept, use the slope to find the next point. The slope is the rise over the run, meaning you go up or down (rise) and then right or left (run) to find the next point. Plot this point and draw a line through the two points. This line is the graph of the equation.

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Key Concepts

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

Linear Equations

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. The general form is Ax + By = C, where A, B, and C are constants. In the given equation, x - 4y = 8, it represents a straight line when graphed on a coordinate plane.

Graphing Linear Equations

Graphing a linear equation involves plotting points that satisfy the equation on a Cartesian plane. To graph x - 4y = 8, one can rearrange it into slope-intercept form (y = mx + b) or find intercepts. The slope indicates the steepness of the line, while the y-intercept shows where the line crosses the y-axis.

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. This form is useful for quickly identifying the line's steepness and where it intersects the y-axis. Converting the given equation into this form can simplify the graphing process.

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