Find the slope of the straight line that passes through the given points or state that the slope is undefined. Then indicate if the line through the points rises (left to right), falls (left to right), is horizontal, or is vertical.
1. (7, 4) and (1, 1)
2. (-3, 4) and (2, -1)
3. (-5, 3) and (-5, 2)
1. (7,4), (1,1).
m = (1-4)/(1-7) = -3/-6=3/6=1/2. Rises.
2. (-3,4), (2,-1).
m = (-1-4)/(2-(-3)) = -5/5 = -1. Falls.
3. (-5,3), (-5,2).
m = (2-3)/(-5-(-5)) = -1/0 = Undefined.
Vertical line.
To find the slope of a straight line passing through two points (x₁, y₁) and (x₂, y₂), you can use the slope formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Let's calculate the slope for each given pair of points:
1. (7, 4) and (1, 1):
Slope = (1 - 4) / (1 - 7) = (-3) / (-6) = 1/2
The line rises from left to right.
2. (-3, 4) and (2, -1):
Slope = (-1 - 4) / (2 - (-3)) = (-5) / (2 + 3) = (-5) / 5 = -1
The line falls from left to right.
3. (-5, 3) and (-5, 2):
The slope is undefined because the change in x is 0. Divide by zero is undefined.
The line is vertical.
Remember, a horizontal line has a slope of 0, a vertical line has an undefined slope, a rising line has a positive slope, and a falling line has a negative slope.