Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y- 3 = (x+ 2); (-2, 3)
To find the equation of a line that is perpendicular to the given line and passes through the given point, we need to determine the slope of the given line and its perpendicular line.
The given line has a slope of 1, which can be determined by comparing the equation to the slope-intercept form y = mx + b, where m is the slope. The equation given can be rewritten as y = x + 5.
Since the line we want is perpendicular to the given line, its slope will be the negative reciprocal of the slope of the given line. The negative reciprocal of 1 is -1/1, or -1.
We now have the slope (-1) and a point (-2, 3) that the line passes through. We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
y - 3 = -1(x - (-2))
y - 3 = -1(x + 2)
y - 3 = -x - 2
Simplifying, we get the equation of the line:
y = -x + 1