Graph x - 3y = 6 by finding the y- and x-intercepts. We will let x = 0 to find the y-intercept of the graph. We will then let y = 0 to find the x-intercept. Since two points determine a line, the y-intercept and x-intercept are enough information to graph this linear equation. x-intercept:y = 0 x - 3y = 6 y-intercept:x = 0 x - 3y = 6. Substitute Substitute - 3y 6. X - 3( = 6 O for x. O for y. -3y = X - To isolate X = y, divide both sides y = The x-intercept is (6, 0). by -3. The y-intercept is (0, -2). Since each intercept of the graph is a solution of the equation, we enter the intercepts in a table of solutions below. As a check, we find one more point on the line. We select a convenient value for x, say, 3, and find the corresponding value of y. х — Зу %3D 6 - 3y = 6 Substitute 3 for x. - Зу %3 To isolate the variable term, -3y, subtract 3 from both sides. y = To isolate y, divide both sides by -3. Therefore, (3, -1) is a solution. It is also entered in the table. We plot the intercepts and the check point, draw a straight line through them, and label the line as х— Зу %3D 6. x - 3y = 6 y (х, у) x – 3y = 6 0 -2 (,-2) + y-intercept (6, 0)

Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter7: Equations And Inequalities In Two Variables
Section7.1: Rectangular Coordinate System And Linear Equations
Problem 43PS
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Graph x – 3y = 6 by finding the y- and x-intercepts.
%D
We will let x
0 to find the y-intercept of the graph. We will then let y
0 to find
the x-intercept.
Since two points determine a line, the y-intercept and x-intercept are enough
information to graph this linear equation.
y-intercept:x
= 0
x-intercept:y = 0
х — Зу 3
6.
х —
— Зу %3D 6
Substitute
Substitute
- Зу
х — 3(
6.
-
%D
O for x.
O for y.
-3y =
X -
To isolate
X =
Y, divide
both sides
y =
The x-intercept is (6, 0).
by -3.
The y-intercept is (0, –2).
Since each intercept of the graph is a solution of the equation, we enter the intercepts in a table of solutions below.
As a check, we find one more point on the line. We select a convenient value for x, say, 3, and find the corresponding value of y.
X -
3y = 6
- 3y = 6
Substitute 3 for x.
— Зу %3
To isolate the variable term, –3y, subtract 3 from both sides.
y =
To isolate y, divide both sides by -3.
Therefore, (3, -1) is a solution. It is also entered in the table.
We plot the intercepts and the check point, draw a straight line through them, and label the line as
х — Зу %3D 6.
y
х — Зу %3D 6
y
(х, у)
x – 3y = 6
-2 (,-2) + y-intercept
(6, 0)
Transcribed Image Text:Graph x – 3y = 6 by finding the y- and x-intercepts. %D We will let x 0 to find the y-intercept of the graph. We will then let y 0 to find the x-intercept. Since two points determine a line, the y-intercept and x-intercept are enough information to graph this linear equation. y-intercept:x = 0 x-intercept:y = 0 х — Зу 3 6. х — — Зу %3D 6 Substitute Substitute - Зу х — 3( 6. - %D O for x. O for y. -3y = X - To isolate X = Y, divide both sides y = The x-intercept is (6, 0). by -3. The y-intercept is (0, –2). Since each intercept of the graph is a solution of the equation, we enter the intercepts in a table of solutions below. As a check, we find one more point on the line. We select a convenient value for x, say, 3, and find the corresponding value of y. X - 3y = 6 - 3y = 6 Substitute 3 for x. — Зу %3 To isolate the variable term, –3y, subtract 3 from both sides. y = To isolate y, divide both sides by -3. Therefore, (3, -1) is a solution. It is also entered in the table. We plot the intercepts and the check point, draw a straight line through them, and label the line as х — Зу %3D 6. y х — Зу %3D 6 y (х, у) x – 3y = 6 -2 (,-2) + y-intercept (6, 0)
4
х — Зу %3D 6
3
X
y
(х, у)
X – 3y = 6
-2
--2) - y-intercept
(6, 0)
3
4
6.
6
(6,
e x-intercept
(3, –1)
3
-1
-1)
e check point
(0,-2)
--4
Check 2
Graph x – 6y = 6 by finding the intercepts.
10
Graph Layers
Clear All
9
8
After you add an object to the graph you
7
Delete
can use Graph Layers to view and edit its
6
properties.
4
Fill
3
2
1
-10 -9
-8
-7
-9
-5
-3
-2
-1
2
3
4
5
6
8.
10
-1
-2
No
-3
Solution
-4
-5
-6
-7
ay 31, 2021, 3:01 PM
2 Help
Transcribed Image Text:4 х — Зу %3D 6 3 X y (х, у) X – 3y = 6 -2 --2) - y-intercept (6, 0) 3 4 6. 6 (6, e x-intercept (3, –1) 3 -1 -1) e check point (0,-2) --4 Check 2 Graph x – 6y = 6 by finding the intercepts. 10 Graph Layers Clear All 9 8 After you add an object to the graph you 7 Delete can use Graph Layers to view and edit its 6 properties. 4 Fill 3 2 1 -10 -9 -8 -7 -9 -5 -3 -2 -1 2 3 4 5 6 8. 10 -1 -2 No -3 Solution -4 -5 -6 -7 ay 31, 2021, 3:01 PM 2 Help
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