To find the equation of the line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
- Calculate the slope (m):
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((0, 3)\) and \((2, 5)\):
- \( (x_1, y_1) = (0, 3) \)
- \( (x_2, y_2) = (2, 5) \)
Now plug in the values: \[ m = \frac{5 - 3}{2 - 0} = \frac{2}{2} = 1 \]
- Find the y-intercept (b):
The y-intercept \( b \) occurs when \( x = 0 \). From the point \((0,3)\), we have: \[ b = 3 \]
- Write the equation:
Now that we have the slope \( m = 1 \) and the y-intercept \( b = 3 \), we can write the equation of the line in slope-intercept form: \[ y = mx + b \]
Substituting in the values, we get: \[ y = 1x + 3 \]
This simplifies to: \[ y = x + 3 \]
Therefore, the equation of the line in slope-intercept form is: \[ \boxed{y = x + 3} \]