Question

y-19=-\frac{13}{9}\left(x+10\right)

Answer 1

To rewrite the given equation \( y - 19 = -\frac{13}{9}(x + 10) \) in a more standard form (e.g., slope-intercept form \( y = mx + b \)), we can follow these steps:

1. Distribute \(-\frac{13}{9}\) on the right side:
\[
y - 19 = -\frac{13}{9}x - \frac{13}{9} \cdot 10
\]
\[
y - 19 = -\frac{13}{9}x - \frac{130}{9}
\]

2. Next, we need to isolate \( y \) by adding 19 to both sides:
\[
y = -\frac{13}{9}x - \frac{130}{9} + 19
\]

3. To add 19 to \(-\frac{130}{9}\), we first convert 19 to a fraction with a common denominator of 9:
\[
19 = \frac{171}{9}
\]

4. Now, we can perform the addition:
\[
y = -\frac{13}{9}x - \frac{130}{9} + \frac{171}{9}
\]
\[
y = -\frac{13}{9}x + \frac{41}{9}
\]

Thus, the equation in slope-intercept form is:
\[
y = -\frac{13}{9}x + \frac{41}{9}
\]