The y-intercept, b, is the value of y when x = 0.
To find the y-intercept, we must first transform the original equation into its slope-intercept form, y = mx + b:
2x - 3y = 24
Subtract 2x on both sides of the equation:
2x - 3y - 2x = -2x + 24
-3y = -2x + 24
Divide both sides of the equation by -3:
[tex]\frac{-3y}{-3} = \frac{-2x + 24}{-3}[/tex]
[tex]y = \frac{2}{3}x - 8[/tex]
Now that we have the equation in its slope-intercept form, we can find the y-intercept by substituting x with 0:
y = -2/3(0)- 8
[tex]y = \frac{2}{3}(0) - 8[/tex]
y = 0 - 8
y = -8
Therefore, the y-intercept is (0, -8), or b = -8
