The slope of the line 4x + 3y – 4 = 0 is :

Q: The slope of the line 4x + 3y – 4 = 0 is :

To determine the slope of the line given by the equation $4x + 3y - 4 = 0$, we need to rewrite the equation in the slope-intercept form, which is $y = mx + b$, where $m$ represents the slope. Let's rearrange the given equation: 1. Start with the original equation: $4x + 3y - 4 = 0$ 2. Solve for $y$ by isolating it on one side of the equation: $3y = -4x + 4$ 3. Divide every term by 3 to solve for $y$: $y = -\frac{4}{3}x + \frac{4}{3}$ From this equation, we can see that the slope $m$ is $-\frac{4}{3}$. Therefore, the correct answer is Option 2: $-\frac{4}{3}$. **Explanation for why each option is incorrect:** 1. **Option 1: $\frac{3}{4}$** This option is incorrect because the slope derived from the equation is $-\frac{4}{3}$, not $\frac{3}{4}$. The sign and the numerator and denominator are reversed. 2. **Option 3: $\frac{4}{3}$** This option is incorrect because the slope is negative, as indicated by the equation. The correct slope is $-\frac{4}{3}$, not $\frac{4}{3}$. 3. **Option 4: $-\frac{3}{4}$** This option is incorrect because the slope derived from the equation is $-\frac{4}{3}$. The values of the numerator and denominator are swapped in this option. In conclusion, the correct slope of the line is $-\frac{4}{3}$, which corresponds to Option 2.

Question

Accepted Answer

To determine the slope of the line given by the equation $4x + 3y - 4 = 0$, we need to rewrite the equation in the slope-intercept form, which is $y = mx + b$, where $m$ represents the slope.

Let's rearrange the given equation:

1. Start with the original equation:  
   $4x + 3y - 4 = 0$

2. Solve for $y$ by isolating it on one side of the equation:  
   $3y = -4x + 4$

3. Divide every term by 3 to solve for $y$:  
   $y = -\frac{4}{3}x + \frac{4}{3}$

From this equation, we can see that the slope $m$ is $-\frac{4}{3}$.

Therefore, the correct answer is Option 2: $-\frac{4}{3}$.

**Explanation for why each option is incorrect:**

1. **Option 1: $\frac{3}{4}$**  
   This option is incorrect because the slope derived from the equation is $-\frac{4}{3}$, not $\frac{3}{4}$. The sign and the numerator and denominator are reversed.

2. **Option 3: $\frac{4}{3}$**  
   This option is incorrect because the slope is negative, as indicated by the equation. The correct slope is $-\frac{4}{3}$, not $\frac{4}{3}$.

3. **Option 4: $-\frac{3}{4}$**  
   This option is incorrect because the slope derived from the equation is $-\frac{4}{3}$. The values of the numerator and denominator are swapped in this option.

In conclusion, the correct slope of the line is $-\frac{4}{3}$, which corresponds to Option 2.