Write the equation of a line that is perpendicular to the given line and that passes through the given point.%0D%0A%0D%0Ay – 3 = (x + 2); (–2, 7)%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0Ay = 5x + 7%0D%0Ay = 5 x + 7%0D%0A%0D%0Ay = 5x + 17%0D%0Ay = 5 x + 17%0D%0A%0D%0Ay = x – 2%0D%0Ay = Image with alt text: one-fifth x – 2%0D%0A%0D%0Ay = –2x + 3
To find the equation of a line that is perpendicular to the given line and passes through the given point, we need to find the slope of the given line and then take the negative reciprocal of that slope.
The given line has a slope of 1.
The negative reciprocal of 1 is -1.
Therefore, the equation of the line perpendicular to the given line and passing through the point (-2, 7) is:
y - 7 = -1(x - (-2))
=> y - 7 = -1(x + 2)
=> y - 7 = -x - 2
=> y = -x + 5
So, the equation of the perpendicular line is y = -x + 5.