Prentice Hall Geometry

Chapter 3 Parallel and Perpendicular Lines > 3-7 Equations of Lines in the Coordinate Plane

Problem 1 Finding Slopes of Lines

Plan

How do you know which numbers go where in a formula?

For slope, you can choose either point's y-coordinate as y sub 2 , . Just be sure to use the same point's x-coordinate as x sub 2 , .

A graph has a line a rising through (2, 3) and (5, 7), line b falling through (negative 1, 2) and (4, negative 2). Line c extends horizontal through (1, 7) and (5, 7). Line d extends vertical through (4, 0) and (4, negative 2).

What is the slope of line b?

m = 2 − ( − 2 ) − 1 − 4 = 4 − 5 = − 4 5 table with 3 rows and 2 columns , row1 column 1 , m , column 2 equals . fraction 2 minus . open , negative 2 , close , over negative 1 minus 4 end fraction , row2 column 1 , , column 2 equals , 4 over negative 5 , row3 column 1 , , column 2 equals negative , 4 fifths , end table
What is the slope of line d?

m = 0 − ( − 2 ) 4 − 4 = 2 0 Undefined table with 2 rows and 2 columns , row1 column 1 , m , column 2 equals . fraction 0 minus . open , negative 2 , close , over 4 minus 4 end fraction , row2 column 1 , , column 2 equals , 2 over 0 . cap undefined , end table

✓ Got It?

Use the graph in Problem 1.
1. What is the slope of line a?
2. What is the slope of line c?

As you saw in Problem 1 and Got It 1 the slope of a line can be positive, negative, zero, or undefined. The sign of the slope tells you whether the line rises or falls to the right. A slope of zero tells you that the line is horizontal. An undefined slope tells you that the line is vertical.

A graph of a positive slope rises from left to right. A graph of a negative slope falls from left to right. A graph of a zero slope is horizontal. A graph of an undefined slope is vertical.

You can graph a line when you know its equation. The equation of a line has different forms. Two forms are shown below. Recall that the y-intercept of a line is the y-coordinate of the point where the line crosses the y-axis.

Take Note Key Concept: Forms of Linear Equations

Definition	Symbols
The slope-intercept form of an equation of a nonvertical line is y = mx + b , y equals mx . plus b , comma where m is the slope and b is the y-intercept.	y = m x + b ↑ ↑ slope y -intercept table with 3 rows and 1 column , row1 column 1 , y equals m x plus b , row2 column 1 , upwards arrow upwards arrow , row3 column 1 , slope , y . minusintercept , end table
The point-slope form of an equation of a nonvertical line is y − y 1 = m ( x − x 1 ) , y minus , y sub 1 . equals m open . x minus , x sub 1 , close . comma where m is the slope and ( x 1 , y 1 ) open , x sub 1 , comma . y sub 1 , close is a point on the line.	y − y 1 = m ( x − x 1 ) ↑ ↑ ↑ y -coordinate slope x -coordinate table with 3 rows and 1 column , row1 column 1 , y minus , y sub 1 , equals m . open . x minus , x sub 1 . close , row2 column 1 , upwards arrow upwards arrow upwards arrow , row3 column 1 , y . minuscoordinate . slope , x . minuscoordinate , end table

End ofPage 190

Problem 1 Finding Slopes of Lines

Plan

✓ Got It?

Take Note Key Concept: Forms of Linear Equations

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