pres Finding slopes of lines parcllel and perpendioular to a line given in the Consider the line $$ 4 x+7 y=5 $$. What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line? Slope of a parallel line: $$ \square $$ Slope of a perpendicular line: $$ \square $$

Question

UpStudy AI · Accepted Answer

To find the slopes of lines parallel and perpendicular to the given line $$ 4x + 7y = 5 $$, we first need to determine the slope of the given line by rewriting it in slope-intercept form $$ y = mx + b $$, where $$ m $$ is the slope.

### Step 1: Rewrite the equation in slope-intercept form

Starting with the equation:
$$
4x + 7y = 5
$$

We can isolate $$ y $$ by following these steps:

1. Subtract $$ 4x $$ from both sides:
   $$
   7y = -4x + 5
   $$

2. Divide every term by $$ 7 $$:
   $$
   y = -\frac{4}{7}x + \frac{5}{7}
   $$

Now, we can see that the slope $$ m $$ of the line is:
$$
m = -\frac{4}{7}
$$

### Step 2: Find the slope of a parallel line

The slope of a line parallel to another line is the same as the slope of the original line. Therefore, the slope of a parallel line is:
$$
\text{Slope of a parallel line} = -\frac{4}{7}
$$

### Step 3: Find the slope of a perpendicular line

The slope of a line perpendicular to another line is the negative reciprocal of the original slope. To find the negative reciprocal of $$ -\frac{4}{7} $$, we take the reciprocal and change the sign:
$$
\text{Slope of a perpendicular line} = \frac{7}{4}
$$

### Final Answers

- Slope of a parallel line: $$ -\frac{4}{7} $$
- Slope of a perpendicular line: $$ \frac{7}{4} $$

Thus, we can fill in the boxes:

Slope of a parallel line: $$ -\frac{4}{7} $$

Slope of a perpendicular line: $$ \frac{7}{4} $$
Slope of a parallel line: $$ -\frac{4}{7} $$ Slope of a perpendicular line: $$ \frac{7}{4} $$

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Algebra Questions