A line that contains the points (0,-2) and (4,0)
a. y=3/2x-8
b. 2y-x=-4
c. y=-3/4x-2
d. -5x+3y=-12
To find the equation of a line passing through two given points, we can use the slope-intercept form equation:
y = mx + b
Where m is the slope of the line and b is the y-intercept.
First, let's find the slope (m) using the given points:
m = (y2 - y1) / (x2 - x1)
m = (0 - (-2)) / (4 - 0)
m = 2 / 4
m = 1/2
Now, let's substitute the slope and one of the points into the slope-intercept form equation to find the y-intercept (b):
-2 = (1/2)(0) + b
-2 = 0 + b
b = -2
So, the equation of the line passing through the points (0, -2) and (4, 0) is:
y = 1/2x - 2
Comparing this equation with the given options:
a. y = 3/2x - 8 (Not the equation of the line passing through the given points)
b. 2y - x = -4 (Not in the slope-intercept form)
c. y = -3/4x - 2 (Not the equation of the line passing through the given points)
d. -5x + 3y = -12 (Not in the slope-intercept form)
The correct answer is none of the given options. The equation of the line passing through the points (0, -2) and (4, 0) is y = 1/2x - 2.