Write an equation in slope-intercept form for the line that passes through the two points.
(6, 3) and (0, -1)
To write an equation in slope-intercept form (y = mx + b) for a line, you first need to calculate the slope of the line, which can be done using the two points (x1, y1) and (x2, y2). The slope (m) is calculated by taking the difference in the y-coordinates and dividing it by the difference in the x-coordinates:
m = (y2 - y1) / (x2 - x1)
Using the points (6, 3) and (0, -1), we can assign (x1, y1) = (6, 3) and (x2, y2) = (0, -1) and then calculate the slope:
m = (-1 - 3) / (0 - 6)
m = (-4) / (-6)
m = 2 / 3
Now that we have the slope, we can use one of the points to solve for the y-intercept (b) in the slope-intercept equation. It's usually easier to use the point where x is 0, if available, because the equation simplifies due to x being zero. However, since we need to show how to use any of the points, let's use (6, 3):
3 = (2/3)(6) + b
Now solve for b:
3 = 4 + b
b = 3 - 4
b = -1
Now that we have both the slope and y-intercept, the slope-intercept form of the line is:
y = (2/3)x - 1
This is the equation of the line that passes through the points (6, 3) and (0, -1).