Determine the slope for the line that meets each condition stated. Show your work.
a.Passes through the points (3,5) and (−1,−7).
b.Passes through the points given by the table of values.
x y
−2 −7
−1 −6
0 −5
1 −4
2 −3
slope = (change in y) / (change in x)
To determine the slope for a line, you can use the formula:
slope = (change in y)/(change in x)
Let's calculate the slope for each scenario:
a. Passes through the points (3,5) and (-1,-7):
First, calculate the change in y:
Δy = (-7) - (5) = -12
Next, calculate the change in x:
Δx = (-1) - (3) = -4
Now, plug the values into the slope formula:
slope = Δy/Δx = -12 / -4 = 3
So, the slope for this line is 3.
b. Passes through the points given by the table of values:
To find the slope using the table of values, choose any two points and use the same slope formula.
Let's take the points (-2, -7) and (0, -5):
Δy = (-5) - (-7) = 2
Δx = 0 - (-2) = 2
Slope = Δy/Δx = 2/2 = 1
So, the slope for this line is 1.
To summarize:
a. The line passing through the points (3,5) and (-1,-7) has a slope of 3.
b. The line passing through the table of values has a slope of 1.