graph the equation 9-x=3/2y using slope intercept form
To graph the equation 9 - x = (3/2)y in slope-intercept form, we need to rearrange the equation to isolate y.
First, subtract 9 from both sides of the equation:
-x = (3/2)y - 9
Next, multiply both sides of the equation by -2/3 to solve for y:
(-2/3)(-x) = (-2/3)(3/2)y + (-2/3)(-9)
(2/3)x = (-3/2)y + 6
Rearranging the equation, we get:
(-3/2)y = (2/3)x - 6
Finally, divide both sides by -3/2 to solve for y:
y = (-2/3)(3/2)x - 6(-3/2)
y = (-1/3)x + 9
Now we have the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
The slope is -1/3 and the y-intercept is 9.
To graph the equation, plot the y-intercept at the point (0,9), and use the slope to find additional points.
Using the slope (rise = -1, run = 3), move down 1 unit and to the right 3 units from the y-intercept:
(0,9) -> (3,8)
(3,8) -> (6,7)
(6,7) -> (9,6)
(9,6) -> (12,5)
(12,5) -> (15,4)
Plotting these points and connecting them, we get the graph of the equation y = (-1/3)x + 9.
To graph the equation 9 - x = (3/2)y in slope-intercept form, we need to rearrange the equation to solve for y.
Step 1: Subtract 9 from both sides:
-x = (3/2)y - 9
Step 2: Multiply both sides by -1 to make the coefficient of x positive:
x = 9 - (3/2)y
Step 3: Divide all terms by (3/2) to isolate y:
(2/3)x = 3 - (2/3)y
Step 4: Subtract 3 from both sides:
(2/3)x - 3 = - (2/3)y
Step 5: Multiply both sides by -1 to make the coefficient of y positive:
-((2/3)x - 3) = y
Step 6: Simplify the equation:
-2x/3 + 6/3 = y
Step 7: Simplify further:
-2x/3 + 2 = y
Now that we have the equation in the slope-intercept form of y = mx + b, where m is the slope and b is the y-intercept, we can identify the values and graph the equation.
In this case, the slope is -2/3, and the y-intercept is 2.
To graph the equation, start by plotting the y-intercept, which is the point (0, 2). Then, use the slope to determine additional points on the line.
For example, from the y-intercept (0, 2), take the slope -2/3. This means that for every three units you move to the right, you move two units down. So, from the point (0, 2), you can move three units to the right and two units down to get the point (3, 0).
You can continue this process to plot more points and then connect them to form a straight line.
To graph the equation 9 - x = (3/2)y in slope-intercept form, we need to isolate y.
9 - x = (3/2)y
First, let's get rid of the fraction by multiplying every term by 2:
2 * (9 - x) = 2 * (3/2)y
18 - 2x = 3y
Now, divide every term by 3 to solve for y:
(18 - 2x)/3 = y
The equation is now in slope-intercept form, y = (18 - 2x)/3. The slope-intercept form is y = mx + b, where m represents the slope and b represents the y-intercept.
For this equation, the slope (m) is -2/3 and the y-intercept (b) is 18/3 = 6.
To graph the equation, follow these steps:
1. Plot the y-intercept at (0, 6). This is the point where the line intersects the y-axis.
2. Use the slope (m) to find additional points. The slope -2/3 means for every increase of 2 in the x-coordinate, the y-coordinate decreases by 3, and vice versa.
- Move 2 units to the right and 3 units down from the y-intercept. Plot this point.
- Move 2 units to the left and 3 units up from the y-intercept. Plot this point as well.
3. Connect the plotted points with a straight line. This line represents the graph of the equation y = (18 - 2x)/3.