Slope of line 17x - 14y - 73 = 0 is equal to :

Q: Slope of line 17x - 14y - 73 = 0 is equal to :

To determine the slope of the line given by the equation $17x - 14y - 73 = 0$, we need to rewrite the equation in the slope-intercept form, which is $y = mx + c$, where $m$ represents the slope of the line. Starting with the given equation: \[ 17x - 14y - 73 = 0 \] We can rearrange it to solve for $y$: \[ -14y = -17x + 73 \] Now, divide every term by $-14$ to isolate $y$: \[ y = \frac{17}{14}x - \frac{73}{14} \] In this form, the coefficient of $x$ is the slope $m$. Therefore, the slope $m$ is $\frac{17}{14}$. Thus, the correct answer is Option 3: $\frac{17}{14}$. **Explanation of Incorrect Options:** 1. **Option 1: $-\frac{17}{14}$** This option is incorrect because the negative sign is not present in the slope when the equation is rearranged into the slope-intercept form. The slope derived from the equation is positive $\frac{17}{14}$, not negative. 2. **Option 2: $\frac{14}{17}$** This option is incorrect because it represents the reciprocal of the correct slope. The slope is determined by the ratio of the coefficients of $x$ and $y$ in the rearranged equation, which is $\frac{17}{14}$, not $\frac{14}{17}$. 3. **Option 4: $-\frac{14}{17}$** This option is incorrect because it not only has the incorrect sign but also represents the reciprocal of the correct slope. The correct slope is $\frac{17}{14}$, not $-\frac{14}{17}$. In conclusion, the correct slope of the line is $\frac{17}{14}$, which is why Option 3 is the correct answer.

Question

Accepted Answer

To determine the slope of the line given by the equation $17x - 14y - 73 = 0$, we need to rewrite the equation in the slope-intercept form, which is $y = mx + c$, where $m$ represents the slope of the line.

Starting with the given equation:

$$ 17x - 14y - 73 = 0 $$

We can rearrange it to solve for $y$:

$$ -14y = -17x + 73 $$

Now, divide every term by $-14$ to isolate $y$:

$$ y = \frac{17}{14}x - \frac{73}{14} $$

In this form, the coefficient of $x$ is the slope $m$. Therefore, the slope $m$ is $\frac{17}{14}$.

Thus, the correct answer is Option 3: $\frac{17}{14}$.

**Explanation of Incorrect Options:**

1. **Option 1: $-\frac{17}{14}$**

This option is incorrect because the negative sign is not present in the slope when the equation is rearranged into the slope-intercept form. The slope derived from the equation is positive $\frac{17}{14}$, not negative.

2. **Option 2: $\frac{14}{17}$**

This option is incorrect because it represents the reciprocal of the correct slope. The slope is determined by the ratio of the coefficients of $x$ and $y$ in the rearranged equation, which is $\frac{17}{14}$, not $\frac{14}{17}$.

3. **Option 4: $-\frac{14}{17}$**

This option is incorrect because it not only has the incorrect sign but also represents the reciprocal of the correct slope. The correct slope is $\frac{17}{14}$, not $-\frac{14}{17}$.

In conclusion, the correct slope of the line is $\frac{17}{14}$, which is why Option 3 is the correct answer.