Question
what is the rate of change of a line that passes through (1,1) and a y intercept of (0,1)
Answers
GPT 3.5
To find the rate of change of a line, we need to determine the slope of the line. The slope is often represented by the letter "m" in the slope-intercept form of a linear equation, which is y = mx + b, where "m" is the slope and "b" is the y-intercept.
Given that the line passes through (1,1) and has a y-intercept of (0,1), we can use these points to find the slope.
Let's label the coordinates of the first point as (x₁, y₁), which in this case is (1,1). The coordinates of the second point will be (x₂, y₂), which is (0,1).
The slope formula is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the given points:
m = (1 - 1) / (0 - 1)
Simplifying:
m = 0 / (-1)
m = 0
Therefore, the rate of change of the line that passes through (1,1) with a y-intercept of (0,1) is 0.
Given that the line passes through (1,1) and has a y-intercept of (0,1), we can use these points to find the slope.
Let's label the coordinates of the first point as (x₁, y₁), which in this case is (1,1). The coordinates of the second point will be (x₂, y₂), which is (0,1).
The slope formula is given by:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the given points:
m = (1 - 1) / (0 - 1)
Simplifying:
m = 0 / (-1)
m = 0
Therefore, the rate of change of the line that passes through (1,1) with a y-intercept of (0,1) is 0.