Write y - 2 = 3/2 (x + 2) in slope-intercept form.
First, distribute the term on the right side of the equation:
y - 2 = (3/2) * (x + 2)
y - 2 = (3/2) * x + (3/2) * 2
y - 2 = (3/2) * x + 3
Next, move the constant term (-2) to the other side of the equation:
y = (3/2) * x + 3 + 2
y = (3/2) * x + 5
Thus, the equation in slope-intercept form is y = (3/2) * x + 5.
Write y - 2 = 3/2 (x + 2) in slope-intercept form.
A. y = 3/2x + 5
B. y = 3/2x + 3/2
C. y = 3/2x + 6
D. y = 3/2 + 5x
To convert the equation y - 2 = 3/2 (x + 2) into slope-intercept form, we need to isolate y on one side of the equation.
First, distribute the 3/2 to both x and 2:
y - 2 = 3/2 * x + 3/2 * 2
This simplifies to:
y - 2 = 3/2 * x + 3
Next, add 2 to both sides of the equation:
y - 2 + 2 = 3/2 * x + 3 + 2
This simplifies to:
y = 3/2 * x + 5
Therefore, the equation in slope-intercept form is y = 3/2 * x + 5.
The correct answer is A. y = 3/2 * x + 5.
Graph the equation 9 - x = 3/2y using slope-intercept form.
To graph the equation 9 - x = 3/2y, we need to rewrite it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Let's solve the equation for y:
9 - x = 3/2y
First, let's isolate y by multiplying both sides of the equation by 2/3:
(9 - x)(2/3) = y
Simplifying, we get:
6 - (2/3)x = y
Therefore, the equation in slope-intercept form is:
y = -(2/3)x + 6.
Now that we have the equation in slope-intercept form, we can identify the slope and y-intercept.
The slope, m, is -2/3, which means that for every increase of 1 in the x-coordinate, the y-coordinate decreases by 2/3.
The y-intercept, b, is 6, which is the point (0, 6) where the line intersects the y-axis.
To plot the graph, we can start by plotting the y-intercept point (0, 6) on the graph. Then, using the slope, we can find more points by moving up 2 units and to the right 3 units, and down 2 units and to the left 3 units.
Here is the graph of the equation:
To write the equation y - 2 = 3/2 (x + 2) in slope-intercept form, we need to isolate y on one side of the equation.
First, distribute 3/2 to (x + 2):
y - 2 = 3/2 * x + 3/2 * 2
Simplifying the right side:
y - 2 = 3/2 * x + 3
Next, let's isolate y by moving the constant term to the other side:
y = 3/2 * x + 3 + 2
Combining the constant terms:
y = 3/2 * x + 5
Therefore, the equation y - 2 = 3/2 (x + 2) in slope-intercept form is y = 3/2 * x + 5.
To write the equation y - 2 = 3/2 (x + 2) in slope-intercept form, we need to isolate y on one side of the equation. The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.
Let's start by distributing the 3/2 to (x + 2):
y - 2 = 3/2 (x + 2)
y - 2 = 3/2 * x + 3/2 * 2
Simplifying further:
y - 2 = 3/2 * x + 3
Now, let's isolate the y term by moving the -2 to the right side of the equation:
y = 3/2 * x + 3 + 2
y = 3/2 * x + 5
So, the equation y - 2 = 3/2 (x + 2) can be written in slope-intercept form as y = 3/2 * x + 5.