The equation provided is:

$y - (-5) = -\frac{5}{7}(x - 14)$

Step-by-Step Simplification

1. Simplify $y - (-5)$ to $y + 5$: $y + 5 = -\frac{5}{7}(x - 14)$

2. Expand the right-hand side: $y + 5 = -\frac{5}{7}x + \frac{70}{7}$

   Simplify the constant term $\frac{70}{7}$ to 10: $y + 5 = -\frac{5}{7}x + 10$

3. Subtract 5 from both sides to isolate $y$: $y = -\frac{5}{7}x + 10 - 5$

   Simplify: $y = -\frac{5}{7}x + 5$

Final Equation

The equation in slope-intercept form is: $y = -\frac{5}{7}x + 5$

Instructions for Graphing

1. Slope: The slope is $-\frac{5}{7}$, meaning for every 7 units you move to the right, the line moves 5 units downward.
2. Y-Intercept: The y-intercept is $5$, meaning the line crosses the y-axis at $y = 5$.

Plotting on the Grid

1. Mark the y-intercept at $(0, 5)$.
2. From that point, use the slope $-\frac{5}{7}$:
   • Move 7 units to the right and 5 units down to $(7, 0)$.
3. Connect the points to draw the line.

Would you like me to graph this equation or provide further explanations?

Related Questions

1. How do you find the slope and intercept from a point-slope form equation?
2. What is the process for converting from point-slope to slope-intercept form?
3. How can the slope of $-\frac{5}{7}$ be interpreted in a real-world context?
4. How do you determine additional points on the line to ensure accurate graphing?
5. What happens if the slope is positive instead of negative?

Tip

When graphing, always double-check the slope direction (positive or negative) to ensure the line’s orientation matches the equation.