Derive the equation of the line in slope-intercept form
(3,0)
(0,-2)
To find the equation of the line passing through the points (3,0) and (0,-2) in slope-intercept form (y = mx + b), we first need to find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) = (3,0) and (x2, y2) = (0,-2)
m = (-2 - 0) / (0 - 3)
m = -2 / -3
m = 2/3
Now that we have the slope, we can use one of the points (3,0) and the slope to find the y-intercept (b). Let's use the point (3,0):
0 = (2/3)(3) + b
0 = 2 + b
b = -2
Now plug the slope (m = 2/3) and y-intercept (b = -2) into the slope-intercept form equation:
y = (2/3)x - 2
Therefore, the equation of the line passing through points (3,0) and (0,-2) in slope-intercept form is:
y = (2/3)x - 2