Answer:
To find an equation of a line that is perpendicular to the line passing through the points (8, 7) and (5, 7), we first need to determine the slope of the original line.
The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) can be calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
For the given points (8, 7) and (5, 7), the slope of the original line is:
m = (7 - 7) / (5 - 8)
= 0 / -3
= 0
Since the slope of the original line is 0, the line is horizontal.
To find the slope of a line perpendicular to this horizontal line, we know that the perpendicular slope is the negative reciprocal of the original slope.
Thus, the slope of the perpendicular line is undefined (or infinite), as any value divided by 0 is undefined.
In point-slope form, an equation of a line is given by:
y - y₁ = m(x - x₁)
Substituting the given point (8, 7) and the undefined slope, the equation becomes:
y - 7 = undefined(x - 8)
As the slope is undefined, we can rewrite the equation as:
x = 8
Therefore, the equation of the line, in point-slope form, that is perpendicular to the line passing through the points (8, 7) and (5, 7) is x = 8.