To derive the equation of a line in slope-intercept form (y = mx + b) using the given points (1, 5) and (0, 3), we first need to find the slope (m) of the line.
The slope \( m \) is calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's denote the points as follows:
- Point 1: \( (x_1, y_1) = (1, 5) \)
- Point 2: \( (x_2, y_2) = (0, 3) \)
Now substitute the values into the slope formula:
\[ m = \frac{3 - 5}{0 - 1} = \frac{-2}{-1} = 2 \]
So, the slope \( m \) of the line is 2.
Next, we need to find the y-intercept \( b \). Since we already have the point \((0, 3)\), which is the y-intercept (where \( x = 0 \)), we can directly see that \( b = 3 \).
Now, plug the slope and y-intercept into the slope-intercept form:
\[ y = mx + b \] \[ y = 2x + 3 \]
Therefore, the equation of the line in slope-intercept form is:
\[ \boxed{y = 2x + 3} \]
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