Slope-intercept form conversion worksheet with eight algebraic equations.

To convert the linear equation from standard form to slope-intercept form, we need to isolate y.

Step 1: Identify the equation.
The given equation is: $10x + 9y = -20$

Step 2: Move the x-term to the other side.
Subtract $10x$ from both sides of the equation to get the $y$ term by itself on the left.
$$9y = -10x - 20$$

Step 3: Isolate y.
Divide every term in the equation by 9 to solve for $y$.
$$y = \frac{-10x}{9} - \frac{20}{9}$$

Step 4: Simplify and format.
Rewrite the equation in the standard slope-intercept form ($y = mx + b$).
$$y = -\frac{10}{9}x - \frac{20}{9}$$

The fraction cannot be simplified further as 10 and 9 share no common factors.

Final Answer:
y = -\frac{10}{9}x - \frac{20}{9}