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 = x – 2 y
To find the equation of a line perpendicular to the given line, we can first find the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope.
The given line has a slope of 1, since the coefficient of x is 1 in the equation y - 3 = x + 2.
A line perpendicular to a line with slope m has a slope of -1/m. In this case, the slope of the perpendicular line is -1/1 = -1.
Now that we have the slope of the perpendicular line, we can use the point-slope form of a line to find the equation. The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (-2, 7) and the slope -1, we substitute these values into the point-slope form:
y - 7 = -1(x - (-2))
y - 7 = -1(x + 2)
y - 7 = -x - 2
y = -x + 5
Therefore, the equation of the line perpendicular to y - 3 = x + 2 and passing through the point (-2, 7) is y = -x + 5.