Find an equation for the line that passes through the points (1,-1) and (-5,1)
To find the equation of the line passing through two given points, we can use the slope-intercept form of a linear equation.
First, we need to find the slope of the line using the formula:
slope (m) = (y2 - y1) / (x2 - x1),
where (x1, y1) = (1, -1) and (x2, y2) = (-5, 1).
Substituting the values into the formula:
slope (m) = (1 - (-1)) / (-5 - 1)
= 2 / -6
= -1/3.
Now that we have the slope (m = -1/3), we can use the point-slope form of the equation:
y - y1 = m(x - x1),
where (x1, y1) = (1, -1).
Substituting the values:
y - (-1) = -1/3(x - 1).
Simplifying:
y + 1 = -1/3x + 1/3.
Rearranging the equation in slope-intercept form:
y = -1/3x + 1/3 - 1
y = -1/3x - 2/3.
Therefore, the equation of the line passing through the points (1, -1) and (-5, 1) is y = -1/3x - 2/3.