Answer:
[tex]y = -\frac{4}{3}x - 9[/tex]
Step-by-step explanation:
The standard form of linear equation is: Ax + By = C, where A, B, and C are integers; A and B ≠ 0, and A is a non-negative integer.
Given the linear equation in standard form, 8x + 6y = -54, we can transform this equation into its slope-intercept form, y = mx + b.
First, subtract 8x from both sides:
8x + 6y = - 54
8x - 8x + 6y = - 8x - 54
6y = -8x - 54
Divide both sides by 6 to isolate y:
[tex]\frac{6y}{6} = \frac{-8x - 54}{6}[/tex]
[tex]y = -\frac{4}{3}x - 9[/tex] ⇒ This is the slope-intercept form where the slope, m = [tex]- \frac{4}{3}[/tex], and the y-intercept, b = -9.
