To derive the equation of the line in slope-intercept form (y = mx + b) using the two points provided, (0, -3) and (1, 1), we need to find the slope (m) and the y-intercept (b).
- Finding the slope (m): The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points:
- \((x_1, y_1) = (0, -3)\)
- \((x_2, y_2) = (1, 1)\)
Substituting in the values:
\[ m = \frac{1 - (-3)}{1 - 0} = \frac{1 + 3}{1} = \frac{4}{1} = 4 \]
So, the slope \(m\) is 4.
- Finding the y-intercept (b): The y-intercept can be found directly from the point (0, -3), which is already in the form (x, y). For the slope-intercept form \(y = mx + b\), when \(x = 0\), \(y\) is equal to \(b\).
Thus, \(b = -3\).
- Writing the equation: Now that we have \(m = 4\) and \(b = -3\), we can write the equation in slope-intercept form:
\[ y = 4x - 3 \]
So, the equation of the line in slope-intercept form is:
\[ \boxed{y = 4x - 3} \]