Write an equation of the line passing through each of the following pairs of points.
(4, 0), (−2, 8)
(4, 0), (-2, 8).
Y = mx + b.
m = (8-0)/(-2-4) = -4/3.
b = y-mx = 0 - (-4/3)4 = 16//3.
To find the equation of a line passing through two given points, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where:
- m represents the slope of the line
- b represents the y-intercept of the line
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's compute the slope using the given points:
- Point 1: (x1, y1) = (4, 0)
- Point 2: (x2, y2) = (-2, 8)
m = (8 - 0) / (-2 - 4)
m = 8 / -6
m = -4/3
Now that we have the slope (m), we can substitute it into the slope-intercept form (y = mx + b) along with one of the given points to solve for b.
Using Point 1 (4, 0):
0 = (-4/3)(4) + b
0 = -16/3 + b
b = 16/3
Therefore, the equation of the line passing through the points (4, 0) and (-2, 8) is:
y = (-4/3)x + 16/3
the slope is 8/-6 = -4/3
So, using the point-slope form,
y = -4/3 (x-4)
or
y-8 = -4/3 (x+2)
you can verify that they describe the same line.