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
y + 3 = –three-eighths(x – 2)
y + 3 = – Image with alt text: three-eighths ( x – 2)
y – 3 = –three-eighths(x + 2)
y – 3 = – Image with alt text: three-eighths ( x + 2)
y – 2 = –three-eighths(x + 3)
y – 2 = – Image with alt text: three-eighths ( x + 3)
y + 3 = three-eighths(x – 2)
To find a line that is perpendicular to the given line, we need to flip the slope and change its sign. The given line has a slope of eight-thirds, so the perpendicular line will have a slope of -3/8.
Now let's use the point-slope form of a linear equation to find the equation of the line:
y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Using the point (-2, 3) and the slope -3/8:
y - 3 = -3/8(x - (-2))
Simplifying:
y - 3 = -3/8(x + 2)
Multiplying both sides by 8 to clear the fraction:
8(y - 3) = -3(x + 2)
8y - 24 = -3x - 6
Rearranging the equation to match a typical slope-intercept form (y = mx + b):
8y = -3x + 18
y = -3/8x + 9/4
So 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