Page 232 - Algebra 1

L E S S O N Locating and Using Intercepts 35
Warm Up
New Concepts
1. Vocabulary A pair of numbers that can be used to locate a point on a
(20)
Evaluate.
2. 3x + 14; x = -9
(16)
Solve.
4. 7x - 18 = -74
(23)
coordinate plane is called a(n) __________.
3. 7.5w - 84.3; w = 15 (16)
5. 57 + 19y = -76 (23)
Linear equations can be graphed by making a table of ordered pairs that satisfy the equation and then graphing the corresponding points (x, y).
An ordered pair or set of ordered pairs that satisfy an equation is called the solution of a linear equation in two variables. When an equation is in standard form, the linear equation can be graphed another way.
The x-coordinate of the point where the graph of an equation intersects the x-axis is called the x-intercept. The y-coordinate of the point where the graph of an equation intersects the y-axis is called the y-intercept. The coordinate pairs (x, 0) and (0, y) that satisfy a linear equation are two solutions of the linear equation in two variables.
Finding x- and y-Intercepts Find the x- and y-intercepts for 3x + 4y = 24.
SOLUTION
To find the intercepts, make a table. Substitute 0 for y and solve for x. Substitute 0 for x and solve for y.
Math Language
An ordered pair can be used to locate a point on a coordinate plane.
Standard Form of a Linear Equation
The standard form of a linear equation is Ax + By = C, where A, B, and C are real numbers and A and B are not both zero.
Example
1
x
y
8
0
0
6
Online Connection www.SaxonMathResources.com
3 x = _2 4 4 y = _2 4 __
33 44 x=8 y=6
The x-intercept is 8. The y-intercept is 6.
3x + 4y = 24 3x + 4(0) = 24 3x = 24
3x + 4y = 24
3(0) + 4y = 24
4y = 24
Lesson 35 217