Which equation is the equation of a line that passes through (-6, 4) and is perpendicular to y= 6x -2?
To find the equation of a line that is perpendicular to another line, we first need to determine the slope of the given line.
The equation of the given line is y = 6x - 2. We can rewrite this equation in slope-intercept form (y = mx + b), where m is the slope of the line. Comparing this equation to the slope-intercept form, we can see that the slope (m) of the given line is 6.
Since the line we are looking for is perpendicular, its slope will be the negative reciprocal of 6. The negative reciprocal of 6 is -1/6.
Now that we have the slope (-1/6) and a point the line passes through (-6, 4), we can use the point-slope form to find the equation of the line. The point-slope form is given by y - y1 = m(x - x1).
Let's substitute the values we have into the point-slope form:
y - 4 = (-1/6)(x - (-6))
Simplifying the equation:
y - 4 = (-1/6)(x + 6)
y - 4 = (-1/6)x - 1
Finally, rearranging the equation to slope-intercept form, we get:
y = (-1/6)x - 1 + 4
y = (-1/6)x + 3
Therefore, the equation of the line that passes through (-6, 4) and is perpendicular to y = 6x - 2 is y = (-1/6)x + 3.