To find the slope-intercept form (y = mx + b) of the line passing through the points \((-5, 0)\) and \((0, 5)\), we first need to determine the slope (m) of the line using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((x_1, y_1) = (-5, 0)\) and \((x_2, y_2) = (0, 5)\):
\[ m = \frac{5 - 0}{0 - (-5)} = \frac{5}{5} = 1 \]
Now that we have the slope \(m = 1\), we can use one of the points to find the y-intercept (b). We can use the point \((0, 5)\):
Since the point \((0, 5)\) corresponds to the y-intercept, we have \(b = 5\).
Now we can write the slope-intercept form of the equation:
\[ y = mx + b \]
Substituting the values of \(m\) and \(b\):
\[ y = 1x + 5 \]
or simply:
\[ y = x + 5 \]
This is the slope-intercept form of the equation of the line.