Find the $$ x $$-intercept and $$ y $$-intercept of the line. $$ 6 x-7 y=-10 $$ $$ y $$-intercept: $$ \square $$

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UpStudy AI · Accepted Answer

1. **Finding the $$ y $$-intercept:**

- Substitute $$ x = 0 $$ into the equation:
     $$
     6(0) - 7y = -10
     $$
   - This simplifies to:
     $$
     -7y = -10
     $$
   - Divide both sides by $$-7$$:
     $$
     y = \frac{-10}{-7} = \frac{10}{7}
     $$
   - Thus, the $$ y $$-intercept is at $$\left(0, \frac{10}{7}\right)$$.

2. **Finding the $$ x $$-intercept:**

- Substitute $$ y = 0 $$ into the equation:
     $$
     6x - 7(0) = -10
     $$
   - This simplifies to:
     $$
     6x = -10
     $$
   - Divide both sides by $$6$$:
     $$
     x = -\frac{10}{6} = -\frac{5}{3}
     $$
   - Thus, the $$ x $$-intercept is at $$\left(-\frac{5}{3}, 0\right)$$.

**Final Answer:**

- $$ y $$-intercept: $$\left(0, \frac{10}{7}\right)$$
- $$ x $$-intercept: $$\left(-\frac{5}{3}, 0\right)$$
The $$ y $$-intercept is at $$ \left(0, \frac{10}{7}\right) $$ and the $$ x $$-intercept is at $$ \left(-\frac{5}{3}, 0\right) $$.

Find the \( x \)-intercept and \( y \)-intercept of the line. \( 6 x-7 y=-10 \) \( y \)-intercept: \( \square \)

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