Graphing Linear

Equations

Chapter 7

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7.1 – The Cartesian Coordinate System and Linear Equations in Two Variables

7.2 – Graphing Linear Equations

7.3 – Slope of a Line

7.4 – Slope-Intercept and Point-Slope Forms

7.5 – Graphing Linear Inequalities7.6 – Functions

Chapter Sections

§ 7.1

The Cartesian Coordinate System

and Linear Equations in Two

Variables

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DefinitionsA graph shows the relationship between two variables in an equation.The Cartesian (rectangular) coordinate system is a grid system used to draw graphs. It is named after its developer, René Descartes (1596-1650).

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Definitions

The two intersecting axis form four quadrants, numbered I through IV.

IVIII

II I

The horizontal axis is called the x-axis.

The vertical axis is called the y-axis.

x

y

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Definitions

The point of intersection of the two axes is called the origin.

Origin

The coordinates, , or the value of the or the value of the xx and the value of the and the value of the yy determines the point. This is also called an ordered pair.

x

y

(0, 0)

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Plotting Points

Plot the point (3, –4).The x-coordinate is 3 and the y-coordinate

is –4.

Starting at the origin, move 3 places to the

right.

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Plotting Points

Plot the point (3, –4).The x-coordinate is 3 and the y-coordinate

is –4.

Then move 4 places down.

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Plotting Points

Plot the point (3, –4).The x-coordinate is 3 and the y-coordinate

is –4.

(3, -4)

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Linear Equations

A linear equation in two variables is an equation that can be put in the form

ax + by = cwhere a, b, and c are real numbers.

This is called the standard form of an equation.of an equation.

Examples:4x – 3y = 12x + 2y = –

35

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Solutions to Equations

The solution to an equation is the ordered pair that can be substituted into the equation without changing the “validity” of the equation.

Is (3, 0) a solution to the equation 4x – 3y = 12?

4x – 3y = 124(3) – 3(0) = 12

12 – 0 = 1212 = 12 Yes, it is a

solution.

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GraphingA graph of an equation is an illustration of a set of points whose coordinates satisfy the equation.

A set of points that are in a straight line are collinear. .

The points (–1, 4), (1, 1) and (4, –3) are collinear.