a line has slope -5/3. Through which two points could this line pass?
To find two points through which the line with a slope of -5/3 could pass, we need the coordinates of these points.
Let's assume the line passes through point A with coordinates (x₁, y₁) and point B with coordinates (x₂, y₂).
Using the formula for slope, we have:
m = (y₂ - y₁) / (x₂ - x₁) = -5/3
Rearranging the formula, we have:
3(y₂ - y₁) = -5(x₂ - x₁)
3y₂ - 3y₁ = -5x₂ + 5x₁
Now, let's choose arbitrary values for x₁, x₂, or y₁, y₂ to find corresponding values for the other variables:
Assume x₁ = 0:
3y₂ - 3y₁ = -5x₂ + 5(0)
3y₂ - 3y₁ = -5x₂
3y₂ - 3y₁ + 5x₂ = 0
If we choose y₁ = 0 and x₂ = 0, we can solve for y₂:
3(0) - 3(0) + 5x₂ = 0
5x₂ = 0
x₂ = 0
Therefore, the line could pass through the points (0, 0) and another point at any value of y₂.
Another example is:
Assume y₁ = 0:
3y₂ - 3(0) = -5x₂ + 5x₁
3y₂ = -5x₂ + 5x₁
y₂ = (-5/3)x₂ + (5/3)x₁
If we choose x₁ = 0 and x₂ = 0, we can solve for y₂:
y₂ = (-5/3)(0) + (5/3)(0)
y₂ = 0
Therefore, the line could pass through the points (0, 0) and (0, y₂), where y₂ can be any value.