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)
To graph the equation 9 - x = 3/2y in slope-intercept form, we need to rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
First, let's isolate y on one side of the equation. Subtract 9 from both sides:
-x = 3/2y - 9
Next, divide both sides by 3/2:
-x / (3/2) = y - 9 / (3/2)
Simplify the equation:
-2/3x = y - 6
Now, add 6 to both sides:
-2/3x + 6 = y
Rearrange the equation in slope-intercept form:
y = -2/3x + 6
Now that we have the equation in slope-intercept form, we can graph it using the given points:
(0, 6) and (3, 4)
Plot the first point (0, 6) on the graph. This point represents the y-intercept (b) since x = 0. The y-coordinate is 6.
Next, use the slope (m) of -2/3. The slope is the ratio of the change in y to the change in x. In this case, for every increase of 3 in x, y decreases by 2.
Starting from the y-intercept (0, 6), move 3 units to the right and 2 units down to find another point.
Plot the second point at (3, 4).
Once you have two points on the graph, you can draw a straight line through them to represent the equation 9 - x = 3/2y.
Note: The other given sets of points (0, 3) (4, 2), (0, 0)(2, 1), (0, -3)(7, -1) are not needed to graph the equation, but you can use them to verify the accuracy of the graph.
To graph the equation 9 - x = (3/2)y in slope-intercept form, we need to isolate y and rearrange the equation to the form y = mx + b, where m is the slope and b is the y-intercept.
Let's solve for y step by step:
1. Start with the equation: 9 - x = (3/2)y
2. Multiply both sides of the equation by 2/3 to isolate y: (2/3)(9 - x) = y
3. Simplify the right side of the equation: (2/3)(9) - (2/3)x = y
→ 6 - (2/3)x = y
→ y = 6 - (2/3)x
Now that we have the equation in slope-intercept form, let's use the given points to plot the graph.
1. (0, 6):
Substitute x = 0 into the equation: y = 6 - (2/3)(0)
Simplify: y = 6
Plot the point (0, 6).
2. (3, 4):
Substitute x = 3 into the equation: y = 6 - (2/3)(3)
Simplify: y = 4
Plot the point (3, 4).
3. (0, 3):
Substitute x = 0 into the equation: y = 6 - (2/3)(0)
Simplify: y = 6
Plot the point (0, 6).
4. (4, 2):
Substitute x = 4 into the equation: y = 6 - (2/3)(4)
Simplify: y = 5.33 (approximately)
Plot the point (4, 5.33).
5. (0, 0):
Substitute x = 0 into the equation: y = 6 - (2/3)(0)
Simplify: y = 6
Plot the point (0, 6).
6. (2, 1):
Substitute x = 2 into the equation: y = 6 - (2/3)(2)
Simplify: y = 4.67 (approximately)
Plot the point (2, 4.67).
7. (0, -3):
Substitute x = 0 into the equation: y = 6 - (2/3)(0)
Simplify: y = 6
Plot the point (0, 6).
8. (7, -1):
Substitute x = 7 into the equation: y = 6 - (2/3)(7)
Simplify: y = 0.67 (approximately)
Plot the point (7, 0.67).
Connect the plotted points with a straight line. That line represents the graph of the equation 9 - x = (3/2)y.
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).