Solution:
Note that:
- Slope = [tex]\frac{2}{3}[/tex]
- Given point: (-6, 2)
- b = y-intercept
To find b, first, we need to identify the standard equation.
- [tex]y - y_{1} = m(x - x_{1} )[/tex]
- => [tex]y - 2 = \frac{2}{3} \{(x - (-6)\}[/tex]
- => [tex]y - 2 = \frac{2}{3} \{x + 6\}[/tex]
- => [tex]y - 2 = \frac{2x}{3} + \frac{12}{3}[/tex]
- => [tex]y = \frac{2x}{3} + 4 + 2[/tex]
- [tex]y = \frac{2x}{3} + 6[/tex]
Now, let's compare the formula with the equation.
- [tex](y = mx + b) = (y = \frac{2x}{3} + 6)[/tex]
- => [tex]b = 6[/tex]
The value of b is 6.
