Give the equation of the line that is perpendicular to the line y=x+4 and passes through point (0, -1).
since it is perpendicular, its slope must be -1 , the negative reciprocal of +1
so the equation must be
y = -x + b
but (0,-1) is the y-intercept, so
y = -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.
The given line has the equation y = x + 4, which is in the slope-intercept form y = mx + b, where m represents the slope. So, the slope of the given line is 1.
To find the slope of the line perpendicular to the given line, we take the negative reciprocal of 1, which is -1.
Now we have the slope (-1) and a point on the line (0, -1). We can use the point-slope form of a line to find the equation of the line. The point-slope form is given as:
y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Substituting the values into the equation:
y - (-1) = -1(x - 0)
y + 1 = -x
Rearranging the equation to the standard form:
x + y + 1 = 0
So, the equation of the line that is perpendicular to y = x + 4 and passes through the point (0, -1) is x + y + 1 = 0.