2x+4y=12 (6,-3) write the slope intrept this is perpinduclar

To find the slope-intercept form of a line perpendicular to the given equation, we first need to determine the slope of the original line.

### Step 1: Find the slope of the original line.
The equation given is:
\[
2x + 4y = 12
\]

To find the slope, we'll first convert this into slope-intercept form (\(y = mx + b\)), where \(m\) is the slope and \(b\) is the y-intercept.

\[
2x + 4y = 12
\]

\[
4y = -2x + 12
\]

\[
y = -\frac{1}{2}x + 3
\]

The slope of the original line is \(-\frac{1}{2}\).

### Step 2: Find the slope of the perpendicular line.
The slope of a line perpendicular to another is the negative reciprocal of the original slope. Therefore:

\[
\text{Perpendicular slope} = -\frac{1}{-\frac{1}{2}} = 2
\]

### Step 3: Write the equation of the perpendicular line passing through the point \((6, -3)\).
We use the point-slope form of a line:

\[
y - y_1 = m(x - x_1)
\]

where \((x_1, y_1) = (6, -3)\) and \(m = 2\).

\[
y - (-3) = 2(x - 6)
\]

\[
y + 3 = 2x - 12
\]

\[
y = 2x - 15
\]

So, the equation of the line perpendicular to \(2x + 4y = 12\) and passing through the point \((6, -3)\) is:

\[
\boxed{y = 2x - 15}
\]

Would you like a detailed explanation on any part of this solution or have further questions?

### Related Questions
1. What is the slope-intercept form of a line parallel to \(2x + 4y = 12\) passing through \((6, -3)\)?
2. How do you convert from slope-intercept form to standard form?
3. If the original slope were positive, how would that affect the slope of the perpendicular line?
4. What is the y-intercept of the line perpendicular to \(2x + 4y = 12\)?
5. How can you determine if two lines are parallel or perpendicular just by looking at their equations?

### Tip
When finding the slope of a perpendicular line, always take the negative reciprocal of the original slope.

Learn how to find the equation of a line perpendicular to 2x + 4y = 12 that passes through the point (6, -3). This detailed solution involves converting to slope-intercept form and using the negative reciprocal of the slope. Suitable for students in Grades 8-10.

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