I'll solve each problem step by step, checking my calculations carefully.
Problem 1: Find the slope of the line that passes through the points (2, 4) and (6, 12)
The slope formula is: m = (y₂ - y₁)/(x₂ - x₁)
Let me label the points:
- Point 1: (x₁, y₁) = (2, 4)
- Point 2: (x₂, y₂) = (6, 12)
m = (12 - 4)/(6 - 2)
m = 8/4
m = 2
Answer: C (2)
Problem 2: Find the slope of the line from the graph
Looking at the graph, I need to identify two points on the line. From the grid, I can see the line passes through:
- (-3, 2) and (0, -1), or
- (-2, 1) and (1, -2)
Let me use (-2, 1) and (1, -2):
m = (-2 - 1)/(1 - (-2))
m = (-3)/(1 + 2)
m = -3/3
m = -1
Answer: B (-1)
Problem 3: Find the slope of the line from the graph
From the grid, I can identify two points on the line:
- (-2, 3) and (2, -2)
m = (-2 - 3)/(2 - (-2))
m = (-5)/(2 + 2)
m = -5/4
Answer: A (-5/4)
Problem 4: Find the slope when given the following points: (2, 5) and (-3, 5)
m = (5 - 5)/(-3 - 2)
m = 0/(-5)
m = 0
When the y-coordinates are the same, we have a horizontal line with slope 0.
Answer: D (0)
Problem 5: What's the slope of the line that passes through (2, -1) and (2, -5)
m = (-5 - (-1))/(2 - 2)
m = (-5 + 1)/(0)
m = -4/0
Division by zero means the slope is undefined. This is a vertical line.
Answer: Undefined
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Final Answer:
1. C (2)
2. B (-1)
3. A (-5/4)
4. D (0)
5. Undefined
Parent Tip: Review the logic above to help your child master the concept of math worksheet algebra 1 9.
