1. a line with a slope of 1/3 passes through the point (3, 6) . which point also lies on this line?
1 answer:
1) Substituting into point-slope form, the equation of the line is y-6=⅓(x-3), which rearranges to:
- y-6 = ⅓x - 1
- y = ⅓x + 5
So, we can now substitute in the coordinates of each of the options to see which point lies on the line.
- 3 = ⅓(6) + 5 -> 3 = 7, which is false.
- 6 = ⅓(7) + 5 -> 6 = 22/3, which is false.
- -3 = ⅓(-3) + 5 -> -3 = 4, which is false.
- 3 = ⅓(-6) + 5 -> 3 = 3, which is true.
So, the answer is (4) (-6, 3)
2) Substituting into point-slope form, the equation of the line is y - 5 = ¾(x-2), which rearranges to:
- y - 5 = 0.75x - 1.5
- y = 0.75x + 3.5
So, we can now substitute in the coordinates of each of the options to see which point lies on the line.
- 8 = 0.75(6)+3.5 -> 8 = 8, which is true.
- 9 = 0.75(5) + 3.5 -> 9 = 7.25, which is false.
- 1 = 0.75(-1) + 3.5 -> 1 = 2.75, which is false.
- 2 = 0.75(6) + 3.5 -> 2 = 8, which is false.
So, the answer is (1) (6, 8).
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Answer:
The rate of change between (1, 5) and (0, -3) would be 8.0.
Step-by-step explanation:
"What is the rate of change between these two points" is the same as asking "what is the slope between these two points".
We are given the two points (1, 5) and (0, -3) and we are asked to find the rate of change (slope) between these two points. To do this, we could use the slope formula to find the rate of change between the two points. The slope formula is:
where (x₂, y₂) and (x₁, y₁) are the two points that we are trying to find the slope between.
Lets make (x₂, y₂) = (1, 5) and (x₁, y₁) = (0, -3). (It does not matter which is (x₂, y₂) and which is (x₁, y₁)). Now plug (x₂, y₂) = (1, 5) and (x₁, y₁) = (0, -3) into the equation:
8 = 8.0, so the answer would be 8.0.
The rate of change between the two points would be 8.0.
I hope you find my answer helpful. :)