Write 0.4x+0.2y=0.6 in slope-intercept form.

Answer 1

To convert the equation \(0.4x + 0.2y = 0.6\) into slope-intercept form, we want to solve for \(y\) in terms of \(x\). The slope-intercept form is given by \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the original equation:

\[ 0.4x + 0.2y = 0.6 \]

1. First, isolate the term with \(y\): \[ 0.2y = 0.6 - 0.4x \]

2. Next, divide every term by \(0.2\) to solve for \(y\): \[ y = \frac{0.6}{0.2} - \frac{0.4x}{0.2} \]

3. Simplify: \[ y = 3 - 2x \]

Now, we have the equation in slope-intercept form:

\[ y = -2x + 3 \]

Thus, the slope \(m\) is \(-2\) and the y-intercept \(b\) is \(3\).

Answer 2

Write the linear equation 3y=6x−18
3
y
=
6
x
−
18
in slope-intercept form.

Answer 3

To convert the equation \(3y = 6x - 18\) to slope-intercept form, we need to solve for \(y\) in terms of \(x\). The slope-intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

Starting with the equation:

\[ 3y = 6x - 18 \]

1. Divide every term by \(3\) to isolate \(y\):

\[ y = \frac{6x}{3} - \frac{18}{3} \]

2. Simplify the fractions:

\[ y = 2x - 6 \]

Now, the equation in slope-intercept form is:

\[ y = 2x - 6 \]

In this equation, the slope \(m\) is \(2\) and the y-intercept \(b\) is \(-6\).

Answer 4

What is the slope and the y
y
-intercept of the equation 9+272x=−32y
9
+
27
2
x
=
−
3
2
y
. Write the y
y
-intercept as an ordered pair.(1 point)

The slope is ___________. The y-intercept is ___________.

Answer 5

To find the slope and the y-intercept of the equation \(9 + 27^2 x = -32y\), we first need to simplify the equation and write it in slope-intercept form \(y = mx + b\).

1. Simplify the equation: First, we calculate \(27^2\): \[ 27^2 = 729 \] So, the equation becomes: \[ 9 + 729x = -32y \]

2. Rearrange to isolate \(y\): Divide each term by \(-32\) to solve for \(y\): \[ y = -\frac{1}{32}(9 + 729x) \] Distributing the \(-\frac{1}{32}\): \[ y = -\frac{9}{32} - \frac{729}{32}x \]

3. Rewrite in standard slope-intercept form: Rearranging gives us: \[ y = -\frac{729}{32}x - \frac{9}{32} \]

4. Identify the slope and y-intercept:

   • The slope \(m\) is \(-\frac{729}{32}\).
   • The y-intercept \(b\) is \(-\frac{9}{32}\), which can be expressed as the ordered pair \((0, -\frac{9}{32})\).

Thus, we conclude:

• The slope is \(-\frac{729}{32}\).
• The y-intercept is \((0, -\frac{9}{32})\).

So, your answers are:

The slope is \(-\frac{729}{32}\). The y-intercept is \((0, -\frac{9}{32})\).