To find the equation of the line that passes through the points (0, 5) and (-3, 17), we will use the slope-intercept form of a linear equation, which is given by:
\[ y = mx + b \]
where \( m \) is the slope and \( b \) is the y-intercept.
Step 1: Calculate the slope (m)
The slope \( m \) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let’s denote the points as follows:
- Point 1: \( (x_1, y_1) = (0, 5) \)
- Point 2: \( (x_2, y_2) = (-3, 17) \)
Substituting the coordinates into the slope formula:
\[ m = \frac{17 - 5}{-3 - 0} = \frac{12}{-3} = -4 \]
Step 2: Use the slope and one point to find the y-intercept (b)
We know that the line passes through (0, 5). Since this point is the y-intercept (where \( x = 0 \)), we can determine the y-intercept \( b \) directly:
\[ b = 5 \]
Step 3: Write the equation of the line
Now that we have the slope \( m = -4 \) and the y-intercept \( b = 5 \), we can write the equation of the line:
\[ y = -4x + 5 \]
Conclusion
The equation of the line that passes through the points (0, 5) and (-3, 17) is
\[ \boxed{y = -4x + 5} \]