Final answer:
The equation of the line that passes through the points (0, -4) and (2, 0) is y = 2x - 4. This is determined by calculating the slope, which is 2, and identifying the y-intercept, which is -4, and applying them to the slope-intercept form y = mx + b.
Step-by-step explanation:
To write the equation of a line in slope-intercept form y = mx + b, we need to find its slope (m) and the y-intercept (b). The slope is calculated as the rise over the run, which is the change in y-coordinates divided by the change in x-coordinates between two points on the line. In this case, the points given are (0, -4) and (2, 0).
The slope is calculated as follows:
m = (y2 - y1) / (x2 - x1)
m = (0 - (-4)) / (2 - 0)
m = 4 / 2
m = 2
Since the line passes through the y-axis at (0, -4), the y-intercept b is -4. Therefore, the equation of the line in slope-intercept form is y = 2x - 4.