Write the equation of the line that passes through the points(3,5) and (−5,−3). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
To find the equation of the line that passes through the points (3,5) and (-5,-3), we can use the formula for the point-slope form of a line:
y - y₁ = m(x - x₁),
where (x₁, y₁) represents the coordinates of one of the given points and m is the slope of the line.
First, let's find the slope using the formula:
m = (y₂ - y₁)/(x₂ - x₁),
where (x₂, y₂) represents the coordinates of the other given point. Plugging the values into the formula, we get:
m = (-3 - 5)/(-5 - 3)
= -8/(-8)
= 1.
So, the slope of the line is 1.
Next, we choose one of the points, let's use (3,5), and substitute its coordinates along with the slope into the point-slope form equation:
y - 5 = 1(x - 3).
Simplifying, we have:
y - 5 = x - 3
y = x - 3 + 5
y = x + 2.
Therefore, the equation of the line that passes through the points (3,5) and (-5,-3) in point-slope form is y = x + 2.