To find the slope of the line given two points and the y-intercept, we can use the formula for slope \( m \):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We have the following points:
- Y-intercept: \( (0, 5) \)
- Another point: \( (3, 3) \)
Using these two points, we can assign:
- \( (x_1, y_1) = (0, 5) \)
- \( (x_2, y_2) = (3, 3) \)
Now, substituting in the values into the slope formula:
\[ m = \frac{3 - 5}{3 - 0} = \frac{-2}{3} \]
So, the slope \( m \) is \( -\frac{2}{3} \).
Now, we can write the equation of the line in slope-intercept form, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
From the information given:
- Slope \( m = -\frac{2}{3} \)
- Y-intercept \( b = 5 \)
Substituting these values into the slope-intercept form, we get:
\[ y = -\frac{2}{3}x + 5 \]
Therefore, the slope of the line is \( -\frac{2}{3} \) and the equation of the line in slope-intercept form is:
\[ y = -\frac{2}{3}x + 5 \]