Find the equation to the straight line passing through
the point (4, 3) and parallel to `3x+4y=12`

Answer

To find the equation of the straight line passing through the point (4, 3) and parallel to the line given by the equation \(3x + 4y = 12\), we will follow these steps:

### Step 1: Determine the slope of the given line
The first step is to find the slope of the line represented by the equation \(3x + 4y = 12\). We can rewrite this equation in the slope-intercept form \(y = mx + c\), where \(m\) is the slope.

Starting with the equation:
\[ 3x + 4y = 12 \]
We can isolate \(y\):
\[ 4y = -3x + 12 \]
Now, divide everything by 4:
\[ y = -\frac{3}{4}x + 3 \]
From this, we can see that the slope \(m\) of the line is:
\[ m = -\frac{3}{4} \]

### Step 2: Use the point-slope form of the line
Since we need to find a line that is parallel to the given line, it will have the same slope. We will use the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
where \((x_1, y_1)\) is the point through which the line passes. In this case, \((x_1, y_1) = (4, 3)\) and \(m = -\frac{3}{4}\).

Substituting these values into the point-slope form:
\[ y - 3 = -\frac{3}{4}(x - 4) \]

### Step 3: Simplify the equation
Now we will simplify the equation:
\[ y - 3 = -\frac{3}{4}x + 3 \]
Adding 3 to both sides gives:
\[ y = -\frac{3}{4}x + 3 + 3 \]
\[ y = -\frac{3}{4}x + 6 \]

### Step 4: Convert to standard form
To convert this equation into standard form \(Ax + By + C = 0\), we can rearrange it:
\[ \frac{3}{4}x + y - 6 = 0 \]
Multiplying through by 4 to eliminate the fraction:
\[ 3x + 4y - 24 = 0 \]

### Final Equation
Thus, the equation of the straight line passing through the point (4, 3) and parallel to the line \(3x + 4y = 12\) is:
\[ 3x + 4y - 24 = 0 \]

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