Find the slope of the line. $$ 3 x-4 y=8 $$ C. Divide both sides of the equation such that the coefficient of $$ y $$ is 1 . D. Find a point on the line. What do the values of $$ m $$ and $$ b $$ represent? A. The number $$ m $$ represents the slope of the line and the number $$ b $$ represents the $$ y $$-intercept. B. The number $$ m $$ represents the slope of the line and the number $$ b $$ represents the $$ x $$-intercept. C. The number $$ m $$ represents the $$ y $$-intercept and the number $$ b $$ represents the slope of the line. D. The number $$ m $$ represents the $$ x $$-intercept and the number $$ b $$ represents the slope of the line. Add the opposite of the $$ y $$-term to both sides. $$ 3 x-4 y=8 $$ $$ 3 x=4 y+8 $$ Subtract the constant term from both sides. $$ 3 x+\pi \square $$

Question

UpStudy AI · Accepted Answer

To determine the **slope** of the line represented by the equation $$ 3x - 4y = 8 $$ and understand the roles of $$ m $$ and $$ b $$ in the slope-intercept form $$ y = mx + b $$, let's follow the steps below:

### 1. **Convert the Equation to Slope-Intercept Form**

The slope-intercept form of a line is given by:
$$ y = mx + b $$
where:
- $$ m $$ is the **slope** of the line.
- $$ b $$ is the **y-intercept** (the point where the line crosses the y-axis).

**Given Equation:**
$$ 3x - 4y = 8 $$

**Step-by-Step Conversion:**
1. **Isolate the $$ y $$-term:**
   $$
   3x - 4y = 8 \quad \Rightarrow \quad -4y = -3x + 8
   $$
   
2. **Divide both sides by -4 to solve for $$ y $$:**
   $$
   y = \frac{-3x + 8}{-4} \quad \Rightarrow \quad y = \frac{3}{4}x - 2
   $$
   
   So, the equation in slope-intercept form is:
   $$
   y = \frac{3}{4}x - 2
   $$

### 2. **Determine the Slope ($$ m $$)**

From the slope-intercept form:
$$
y = \frac{3}{4}x - 2
$$
- The coefficient of $$ x $$ is $$ \frac{3}{4} $$, which represents the **slope** ($$ m $$).

**Therefore, the slope $$ m = \frac{3}{4} $$.**

### 3. **Understanding $$ m $$ and $$ b $$**

**Question: What do the values of $$ m $$ and $$ b $$ represent?**

**Options:**
- **A.** The number $$ m $$ represents the slope of the line and the number $$ b $$ represents the $$ y $$-intercept.
- **B.** The number $$ m $$ represents the slope of the line and the number $$ b $$ represents the $$ x $$-intercept.
- **C.** The number $$ m $$ represents the $$ y $$-intercept and the number $$ b $$ represents the slope of the line.
- **D.** The number $$ m $$ represents the $$ x $$-intercept and the number $$ b $$ represents the slope of the line.

**Correct Answer:**
- **A.** The number $$ m $$ represents the slope of the line and the number $$ b $$ represents the $$ y $$-intercept.

**Explanation:**
- In the slope-intercept form ($$ y = mx + b $$):
  - **$$ m $$** is the **slope**, indicating the steepness and direction of the line.
  - **$$ b $$** is the **y-intercept**, indicating where the line crosses the y-axis.

### 4. **Summary of Steps Taken**

1. **Add the Opposite of the $$ y $$-Term to Both Sides:**
   $$
   3x - 4y = 8 \quad \Rightarrow \quad 3x = 4y + 8
   $$
   
2. **Subtract the Constant Term from Both Sides to Isolate $$ y $$:**
   $$
   4y = 3x - 8 \quad \Rightarrow \quad y = \frac{3}{4}x - 2
   $$
   
By following these steps, we've successfully found the slope of the line and clarified the roles of $$ m $$ and $$ b $$ in the equation.
The slope of the line is $$ \frac{3}{4} $$. The number $$ m $$ represents the slope of the line, and the number $$ b $$ represents the $$ y $$-intercept.

Solución de tutoría real

Responder

Solución

Extra Insights

preguntas relacionadas

Latest Algebra Questions