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)
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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