passes through (3,-2) and (-3,4)
To find the equation of a line that passes through two given points, we can use the point-slope form of a linear equation:
(y - y1) = m(x - x1)
Where:
- (x1, y1) represents one of the given points on the line
- m represents the slope of the line
To find the slope (m), we can use the formula:
m = (y2 - y1) / (x2 - x1)
where:
- (x1, y1) represents the coordinates of the first given point
- (x2, y2) represents the coordinates of the second given point
Given points:
Point 1: (x1, y1) = (3, -2)
Point 2: (x2, y2) = (-3, 4)
Substituting the values into the slope formula:
m = (4 - (-2)) / (-3 - 3)
m = (4 + 2) / (-6)
m = 6 / (-6)
m = -1
Now that we have the slope (m = -1) and one of the given points (3, -2), we can substitute these values into the point-slope form equation:
(y - (-2)) = -1(x - 3)
Simplifying:
(y + 2) = -x + 3
Rearranging to slope-intercept form (y = mx + b):
y = -x + 1
Therefore, the equation of the line that passes through (3, -2) and (-3, 4) is y = -x + 1.