Graph the equation 9 - x = 3/2y using slope intercept form!
To graph the equation 9 - x = (3/2)y using slope-intercept form, we need to rearrange the equation to isolate y.
Starting with:
9 - x = (3/2)y
We can multiply both sides of the equation by 2/3 to isolate y:
(2/3)(9 - x) = (2/3)(3/2)y
(2/3)(9) - (2/3)(x) = (2/3)(3/2)y
6 - (2/3)x = (1/2)y
Now we can rewrite the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept:
y = (1/2)y + 6 - (2/3)x
Rearranging the terms, we get:
y - (1/2)y = 6 - (2/3)x
(1/2)y = (2/3)x + 6
Multiplying through by 2, we have:
y = (4/3)x + 12
Now we can graph the equation y = (4/3)x + 12.
To graph the equation, plot the y-intercept at (0, 12). The slope of the line is 4/3, which means for every 3 units moved to the right, the line moves up 4 units.
Plot a second point on the line by moving 3 units to the right and 4 units up from the y-intercept. This point is at (3, 16).
Draw a straight line through these two points to represent the equation y = (4/3)x + 12.
The graph of the equation 9 - x = (3/2)y is a straight line with a slope of 4/3 and a y-intercept of 12.
To graph the equation 9 - x = (3/2)y in slope-intercept form, we need to rearrange the equation to isolate y.
Step 1: Start with the given equation:
9 - x = (3/2)y
Step 2: Distribute the (3/2) to y:
9 - x = (3/2)y
9 - x = (3/2)y
(2/3)(9 - x) = y
Step 3: Simplify:
(2/3)(9) - (2/3)(x) = y
6 - (2/3)x = y
Now we have the equation in the slope-intercept form: y = mx + b
Where m is the slope and b is the y-intercept.
In this case, the slope (m) is -(2/3) and the y-intercept (b) is 6.
Therefore, the slope-intercept form of the equation is:
y = -(2/3)x + 6
To graph the equation, start at the y-intercept of 6 on the y-axis, and then use the slope -(2/3) (which means for every 3 units you move right, you move 2 units down) to plot additional points and draw the line.
To graph the equation 9 - x = (3/2)y in slope-intercept form, we need to isolate y on one side of the equation.
Given equation: 9 - x = (3/2)y
First, we can rearrange the equation to isolate y on one side:
x - 9 = -(3/2)y
Next, we can divide both sides of the equation by -(3/2) to solve for y:
(y intercept form) -> y = (-2/3)(x - 9)
To graph this equation, we start by identifying the slope (coefficient of x) and the y-intercept, which is -b/a, where a is the coefficient of x and b is the constant term.
Given equation: y = (-2/3)(x - 9)
From this equation, we observe that the slope is (-2/3), and the y-intercept is -b/a = -(-9)/(2/3) = 9*(3/2) = 27/2 = 13.5.
Now, we can plot the y-intercept (0, 13.5) on the graph. Then, using the slope, we can move from the y-intercept to another point on the line. The slope -2/3 means that for every 2 units to the right on the x-axis, we move down 3 units on the y-axis.
Once you have two points, you can draw a straight line passing through them to graph the equation.
Let's choose another point to make it easier. Let's assume x = 6.
Substituting x = 6 into the equation:
y = (-2/3)(6 - 9) = (-2/3)(-3) = 2
So, another point on the line is (6, 2).
Now, we can plot these two points: (0, 13.5) and (6, 2).
Finally, draw a straight line passing through these two points.
Note: Make sure to label the axes and indicate the scale to accurately represent the graph.