Give the equation of the line y=x+6 that is perpendicular to the line and passes through point (0, -4).
To find the equation of the line perpendicular to y = x + 6, we need to determine its slope first. The given line is in the form y = mx + b, where m represents the slope. In this case, the slope is 1.
The perpendicular line will have a slope that is the negative reciprocal of 1. To find the negative reciprocal, we take the reciprocal of 1 (which is 1) and then change its sign. Therefore, the slope of the perpendicular line is -1.
Now that we have the slope (-1) and a point that the line passes through (0, -4), we can use the point-slope form of a line to find its equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents the given point and m represents the slope. Plugging in the values, we get:
y - (-4) = -1(x - 0)
Simplifying further, we have:
y + 4 = -x
To obtain the equation in the standard form (Ax + By + C = 0), we bring all terms to one side:
x + y + 4 = 0
Therefore, the equation of the line perpendicular to y = x + 6 and passing through the point (0, -4) is x + y + 4 = 0.