Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y – 3 = eight-thirds(x + 2); (–2, 3)
(1 point)
Responses
To find the equation of a line that is perpendicular to the given line and passes through the point (-2, 3), we first need to find the slope of the given line. The given line has a slope of 8/3.
Since the line we are looking for is perpendicular to the given line, its slope will be the negative reciprocal of 8/3. The negative reciprocal of 8/3 is -3/8.
Now we can use the point-slope form of the equation of a line to find the equation of the line:
y - y₁ = m(x - x₁)
Using the point (-2, 3) and the slope -3/8, we have:
y - 3 = -3/8(x + 2)
y - 3 = -3/8x - 3/4
y = -3/8x + 9/4
Therefore, the equation of the line that is perpendicular to the given line and passes through the point (-2, 3) is:
y = -3/8x + 9/4