The slope of the line passing through points x sub 1, y sub 1 and x sub 2 y sub 2 is found using the formula the quantity y sub 2 minus Y sub 1 over the quantity X sub two minus X sub one the line passing through the points, 32 and two why is perpendicular to a line that has a slope of 1 over three what is the value of Y?
To find the slope of the line passing through points (x₁, y₁) and (x₂, y₂), we use the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Given the points (32, 2) and a slope of 1/3 for another line, we need to find the slope of the line perpendicular to the given line.
The slope of a line perpendicular to another line is the negative reciprocal of the given line's slope.
So, the slope of the line perpendicular to the line with a slope of 1/3 is -3/1, or simply -3.
Using the given points and the slope of -3, we can find the equation of the perpendicular line using the point-slope form:
(y - y₁) = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
Plugging in x₁ = 32, y₁ = 2, and m = -3:
(y - 2) = -3(x - 32)
Expanding and re-arranging the equation:
y - 2 = -3x + 96
Moving -3x to the left side:
3x + y = 98
The value of y in this equation is equal to 98 minus 3 times x.