Equation of line passing through the point (4,3) and parallel to the line, 6y=8x+7 is?*

5 points

4x-3y=7

3x-4y=7

3x+4y=0

3x+4y=24

To find the equation of the line passing through the point \((4, 3)\) and parallel to the line \(6y = 8x + 7\), let's follow these steps:

### Step 1: Simplify the given line equation
First, simplify the equation \(6y = 8x + 7\) to the slope-intercept form \(y = mx + c\).

\[
6y = 8x + 7
\]
\[
y = \frac{8}{6}x + \frac{7}{6}
\]
\[
y = \frac{4}{3}x + \frac{7}{6}
\]

Here, the slope \(m\) of the given line is \(\frac{4}{3}\).

### Step 2: Find the equation of the new line
Since the new line is parallel to the given line, it will have the same slope \(m = \frac{4}{3}\). 

The equation of a line in point-slope form is:

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

Substituting the given point \((4, 3)\) and the slope \(m = \frac{4}{3}\) into the equation:

\[
y - 3 = \frac{4}{3}(x - 4)
\]

### Step 3: Simplify the equation
Multiply both sides by 3 to eliminate the fraction:

\[
3(y - 3) = 4(x - 4)
\]
\[
3y - 9 = 4x - 16
\]

Rearrange the equation to the standard form \(Ax + By = C\):

\[
4x - 3y = 7
\]

### Step 4: Compare with the options
The equation we derived is \(4x - 3y = 7\).

Thus, the correct answer is:

**(1) \(4x - 3y = 7\)**

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Would you like more details or have any questions? Here are some related questions:

1. How do you find the equation of a line given two points?
2. What is the slope-intercept form of a line?
3. How do you determine if two lines are parallel?
4. How do you convert a line equation from point-slope form to standard form?
5. What is the general form of a linear equation?

**Tip:** When two lines are parallel, their slopes are always equal.

Learn how to find the equation of a line parallel to 6y = 8x + 7 passing through the point (4, 3). Detailed step-by-step solution provided. Suitable for high school students studying linear equations and parallel lines.

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