To write the equation of a line in slope-intercept form (y = mx + b) given a slope \( m \) and a point \((x_1, y_1)\), we can use the point-slope form of the equation, which is:
\[ y - y_1 = m(x - x_1) \]
Given:
- Slope \( m = \frac{8}{3} \)
- Point \( (x_1, y_1) = (2, 3) \)
Substituting these values into the point-slope formula:
\[ y - 3 = \frac{8}{3}(x - 2) \]
Now, simplify this equation:
- Distribute the slope on the right side:
\[ y - 3 = \frac{8}{3}x - \frac{16}{3} \]
- Add 3 to both sides to solve for \( y \):
\[ y = \frac{8}{3}x - \frac{16}{3} + 3 \]
- Convert 3 into a fraction with a denominator of 3:
\[ 3 = \frac{9}{3} \]
So,
\[ y = \frac{8}{3}x - \frac{16}{3} + \frac{9}{3} \]
- Combine the constant terms:
\[ y = \frac{8}{3}x - \frac{7}{3} \]
Thus, the equation of the line in slope-intercept form is:
\[ y = \frac{8}{3}x - \frac{7}{3} \]