Ben and phoebe are finding the slope of a line. Ben chose two points on the line and used them to find the slope, phoebe used two different points to find
the slope. did they get the same answer? explain.
Unless somebody made a calculation error, they will obtain the same answer, since for a straight line, the slope is always the same, no matter where you take the slope.
Yes they’ve had the same answer
To determine if Ben and Phoebe got the same answer when finding the slope of a line, we need to understand how to calculate slope using two points.
The slope of a line is the measure of how steep or slanted the line is. It represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.
The formula to find the slope (m) between two points (x₁, y₁) and (x₂, y₂) on a line is:
m = (y₂ - y₁) / (x₂ - x₁)
If Ben and Phoebe used different points, it's possible that they could get different slope values. This would depend on the specific points they chose.
For example, let's say Ben chose the points (1, 2) and (3, 4) to find the slope. By applying the formula:
m (Ben) = (4 - 2) / (3 - 1)
m (Ben) = 2 / 2
m (Ben) = 1
Now, let's assume Phoebe chose different points on the same line, such as (2, 3) and (4, 6). Applying the formula:
m (Phoebe) = (6 - 3) / (4 - 2)
m (Phoebe) = 3 / 2
m (Phoebe) = 1.5
As you can see, Ben and Phoebe obtained different slope values. Therefore, depending on the points they chose, they might not have gotten the same answer.
To conclude, the answer to whether Ben and Phoebe got the same answer for the slope of the line depends on the specific points they selected.