The problem shows two points, $(5, -9)$ and $(3, -2)$. I will assume you are asking to find the equation of the line passing through these points or the slope. Let me proceed with the slope calculation and equation derivation:

Step 1: Calculate the slope ($m$):

The slope formula is: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the points $(x_1, y_1) = (5, -9)$ and $(x_2, y_2) = (3, -2)$: $m = \frac{-2 - (-9)}{3 - 5} = \frac{-2 + 9}{-2} = \frac{7}{-2} = -\frac{7}{2}$

Step 2: Write the equation of the line ($y = mx + b$):

We use the point-slope form of the equation: $y - y_1 = m(x - x_1)$

Substituting $m = -\frac{7}{2}$, and using $(x_1, y_1) = (5, -9)$: $y - (-9) = -\frac{7}{2}(x - 5)$ $y + 9 = -\frac{7}{2}x + \frac{35}{2}$

Simplify: $y = -\frac{7}{2}x + \frac{35}{2} - 9$ $y = -\frac{7}{2}x - \frac{43}{2}$

Final Equation:

$y = -\frac{7}{2}x - \frac{43}{2}$

Would you like additional explanation or help solving further?

Related Questions:

1. How do you find the midpoint between these two points?
2. Can we convert this slope-intercept equation to standard form?
3. What is the perpendicular slope for this line?
4. How do you calculate the distance between these two points?
5. How does the slope impact the steepness of the line?

Tip:

Always simplify fractions and double-check signs when using coordinates in equations!