Write the equation of a line perpendicular to the given line and passing through the given point. y – 3 = (x + 2); (–2, 7) of these options y = 5x + 7 y = 5 x + 7 y = 5x + 17 y = 5 x + 17 y = x – 2 y
To find the equation of a line perpendicular to the given line, we need to find the negative reciprocal of the slope of the given line.
The given line has a slope of 1. To find the negative reciprocal of the slope, we take the negative of 1 and flip it, giving us -1.
Now we have the slope of the line perpendicular to the given line.
We also have a point that the line needs to pass through, which is (-2, 7).
Using the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the point and m is the slope, we can plug in the values to find the equation.
Using (-2, 7) as (x1, y1) and -1 as the slope, the equation of the line perpendicular to the given line and passing through the point (-2, 7) is:
y - 7 = -1(x - (-2))
Simplifying this equation gives us:
y - 7 = -1(x + 2)
y - 7 = -x - 2
Adding x to both sides:
y + x - 7 = -2
Rearranging the terms:
y + x = -2 + 7
y + x = 5
Therefore, the correct equation of the line perpendicular to y - 3 = x + 2 and passing through (-2, 7) is y + x = 5.