find the equation of the line that is perpendicular to y=-3x-6; (-1,5)?
your line has slope -3
perp line has slope 1/3
So, now you have a point and a slope, so the line is
y-5 = 1/3 (x+1)
To find the equation of a line that is perpendicular to another line, we need to determine the slope of the given line and then find the negative reciprocal of that slope. We can use the slope-intercept form of a line, which is given by y = mx + b, where m is the slope and b is the y-intercept.
The given line is y = -3x - 6. Comparing this equation with the slope-intercept form, we see that the slope (m) of this line is -3.
To find the slope of the line perpendicular to this line, we take the negative reciprocal of -3. The negative reciprocal of a number a is -1/a. Therefore, the slope of the line perpendicular to the given line is -1/(-3), which simplifies to 1/3.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find the equation. The point-slope form is given by (y - y1) = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
The point given in the question is (-1, 5), so we substitute these values into the point-slope form and the slope we found: (y - 5) = (1/3)(x - (-1)).
Simplifying this equation will give us the final equation in either slope-intercept form or general form.