Write y−2=3/2(x+2) in slope-intercept form.

Answer 1

To write the equation in slope-intercept form, we need to isolate y on one side of the equation.

Starting with the given equation, we can distribute the 3/2 to the terms inside the parentheses:

y - 2 = (3/2)(x + 2)

Simplifying this equation further,

y - 2 = (3/2)x + 3

Next, we can isolate y by adding 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 y - 2 = (3/2)(x + 2) in slope-intercept form is y = (3/2)x + 5.

Answer 2

Identify the slope and the y -intercept of the equation 4x−3y=12 .

Answer 3

To identify the slope and y-intercept of the equation 4x - 3y = 12, we need to rearrange the equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

First, let's isolate the y term by subtracting 4x from both sides of the equation:

-3y = -4x + 12

Next, divide both sides of the equation by -3 to solve for y:

y = (4/3)x - 4

Now we can identify the slope and y-intercept.

The slope (m) is the coefficient of x, which is 4/3.
The y-intercept (b) is the constant term, which is -4.

So, the slope of the equation is 4/3 and the y-intercept is -4.