Give the equation of the line that is perpendicular to the line y = x + 4 and passes through point (0,-1).
A) y = x - 1
B) y = x + 1
C) y = -x + 1
D) y = -x - 1
So if passes through point o,-1 does that mean that the answer has to be negative? Answer A
Answer A is not correct!
The line y=mx+c that is perpendicular to
y=x+4
has to have the slope equal to the negative of the reciprocal of the given line, i.e. m=-1/(1)=-1
Secondly, since it passes through (x1,y1)=(0,-1), we have
(y-y1)=m(x-x1) where m=-1
(y-(-1))=-1(x-0)
Can you now figure out which is the right one?
Feel free to post your answer for confirmation.
hmm. so I'm assuming it's C then correct!!
To find the equation of a line that is perpendicular to the line y = x + 4 and passes through point (0, -1), we need to determine the slope of the given line.
The given line y = x + 4 is in slope-intercept form y = mx + b, where m represents the slope. In this case, the slope of the given line is 1.
The slope of a line perpendicular to another line is the negative reciprocal of the slope of the given line. In this case, the slope of the line perpendicular to y = x + 4 is -1.
Now that we have the slope (-1) and a point (0, -1), we can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form of a linear equation is y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Plugging in the values, we have:
y - (-1) = -1(x - 0)
y + 1 = -x
y = -x - 1
Therefore, the equation of the line that is perpendicular to y = x + 4 and passes through point (0, -1) is y = -x - 1, which matches option D).