Which equation represents a line which is parallel to the line y, equals, minus, start fraction, 4, divided by, 3, end fraction, x, minus, 7*y*=−34​*x*−7?

Answer

Multiple Choice Answers

3, x, minus, 4, y, equals, minus, 163*x*−4*y*=−16

3, y, minus, 4, x, equals, 183*y*−4*x*=18

3, x, plus, 4, y, equals, 203*x*+4*y*=20

4, x, plus, 3, y, equals, minus, 184*x*+3*y*=−18




To determine which equation represents a line that is parallel to the given line \( y = -\frac{4}{3}x - 7 \), we need to consider the slope of the line.

### Step 1: Identify the slope of the given line
The given line is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope. For the equation \( y = -\frac{4}{3}x - 7 \), the slope \( m \) is \( -\frac{4}{3} \).

### Step 2: Identify parallel lines
Two lines are parallel if they have the same slope. Therefore, we are looking for an equation where the slope is also \( -\frac{4}{3} \).

### Step 3: Analyze the multiple-choice options
Let's check each option to see if it has a slope of \( -\frac{4}{3} \).

1. **Option A:** \( 3x - 4y = -16 \)
   - Rearrange to slope-intercept form: 
     \[
     -4y = -3x - 16
     \]
     \[
     y = \frac{3}{4}x + 4
     \]
     - Slope: \( \frac{3}{4} \) (not \( -\frac{4}{3} \))

2. **Option B:** \( 3y - 4x = 18 \)
   - Rearrange to slope-intercept form: 
     \[
     3y = 4x + 18
     \]
     \[
     y = \frac{4}{3}x + 6
     \]
     - Slope: \( \frac{4}{3} \) (not \( -\frac{4}{3} \))

3. **Option C:** \( 3x + 4y = 20 \)
   - Rearrange to slope-intercept form: 
     \[
     4y = -3x + 20
     \]
     \[
     y = -\frac{3}{4}x + 5
     \]
     - Slope: \( -\frac{3}{4} \) (not \( -\frac{4}{3} \))

4. **Option D:** \( 4x + 3y = -18 \)
   - Rearrange to slope-intercept form: 
     \[
     3y = -4x - 18
     \]
     \[
     y = -\frac{4}{3}x - 6
     \]
     - Slope: \( -\frac{4}{3} \) (this is correct)

### Conclusion
The correct answer is **Option D**: \( 4x + 3y = -18 \).

Would you like any more details or have any questions? 

Here are 5 follow-up questions:
1. What is the general form of a linear equation?
2. How do you convert from standard form to slope-intercept form?
3. What is the relationship between perpendicular lines in terms of slope?
4. How would you determine if two lines are the same line?
5. Can you find the y-intercept of the line \( y = -\frac{4}{3}x - 7 \)?

**Tip:** When finding the slope from the standard form, always isolate the \( y \)-term to convert the equation into slope-intercept form.

Learn how to identify a line parallel to y = -4/3x - 7 with a detailed explanation and step-by-step solution. This problem involves understanding parallel lines and using slope-intercept form. Suitable for Grades 7-9.

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