To graph the equation 9 - x = (3/2)y using slope-intercept form, we need to express the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Given equation: 9 - x = (3/2)y
First, isolate y by moving the x term to the other side of the equation:
-x = (3/2)y - 9
Next, divide both sides by (3/2) to isolate y:
(-2/3)(-x) = y - 9
(2/3)x = y - 9
Now, add 9 to both sides:
(2/3)x + 9 = y
The equation is now in slope-intercept form: y = (2/3)x + 9.
Now, we can plot the points and graph the equation:
(0, 6): Substituting x = 0 into the equation, we get y = (2/3)(0) + 9 = 9. The point is (0, 9).
(3, 4): Substituting x = 3 into the equation, we get y = (2/3)(3) + 9 = 11/3. The point is (3, 11/3).
(0, 3): Substituting x = 0 into the equation, we get y = (2/3)(0) + 9 = 9. The point is (0, 9).
(4, 2): Substituting x = 4 into the equation, we get y = (2/3)(4) + 9 = 14/3. The point is (4, 14/3).
(0, 0): Substituting x = 0 into the equation, we get y = (2/3)(0) + 9 = 9. The point is (0, 9).
(2, 1): Substituting x = 2 into the equation, we get y = (2/3)(2) + 9 = 19/3. The point is (2, 19/3).
(0, -3): Substituting x = 0 into the equation, we get y = (2/3)(0) + 9 = 9. The point is (0, 9).
(7, -1): Substituting x = 7 into the equation, we get y = (2/3)(7) + 9 = 25/3. The point is (7, 25/3).
Graphing these points and connecting them with a straight line, we get the following graph:
Answer: The graph of the equation 9 - x = (3/2)y is a straight line that passes through the points (0, 9), (3, 11/3), (4, 14/3), (2, 19/3), and (7, 25/3).
graph the equation 9-x=3/2y using slope intercept form
(0,6) (3,4)
(0,3) (4,2)
(0,0)(2,1)
(0,-3)(7,-1)
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