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

Graphs and Coordinates

College Algebra

2. Graphs of Equations

Graphs and Coordinates

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1:48 minutes

Problem 16

Textbook Question

Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3y = x + 2

Verified step by step guidance

Identify the given equation: y = x + 2. This is a linear equation, which means its graph will be a straight line.

Create a table of values for x and y. Use the given x-values (-3, -2, -1, 0, 1, 2, 3). For each x-value, substitute it into the equation y = x + 2 to calculate the corresponding y-value.

For example, when x = -3, substitute into the equation: y = -3 + 2. Similarly, calculate y for all other x-values.

Plot the points (x, y) on a coordinate plane. Each pair of x and y values forms a point, such as (-3, -1), (-2, 0), etc.

Draw a straight line through all the plotted points. Since this is a linear equation, the points should align perfectly, forming a straight line.

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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 expression that represents a straight line when graphed on a coordinate plane. It typically takes the form y = mx + b, where m is the slope and b is the y-intercept. Understanding linear equations is essential for graphing, as it allows students to identify the relationship between variables and predict values.

Graphing Points

Graphing points involves plotting specific coordinates on a Cartesian plane, where the x-coordinate indicates the horizontal position and the y-coordinate indicates the vertical position. For the equation y = x + 2, students will calculate y for given x values, such as -3, -2, -1, etc., and plot these points to visualize the linear relationship.

Slope and Y-Intercept

The slope of a line indicates its steepness and direction, calculated as the change in y over the change in x (rise/run). The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x is zero. In the equation y = x + 2, the slope is 1 and the y-intercept is 2, which are crucial for understanding the line's behavior and graphing it accurately.