A family of curves with a slope of 1 at (1,1) refers to a group of curves on a graph where each curve has a slope of 1 at the point (1,1). This means that the tangent line to each curve at the point (1,1) will have a slope of 1.
To graph a family of curves with a slope of 1 at (1,1), you can start by plotting the point (1,1) on the coordinate plane. Then, using the slope-intercept form of a line, you can draw a line with a slope of 1 passing through the point (1,1). This line will represent one curve in the family. To graph the other curves, you can use the slope-intercept form again but with different y-intercepts. This will give you a family of parallel lines with a slope of 1 at (1,1).
A slope of 1 at (1,1) in a family of curves indicates that all the curves in the family have the same rate of change at the point (1,1). This can be useful in modeling real-world scenarios, as it allows for easy comparison and analysis of different curves.
Yes, a family of curves can have a slope of 1 at a point other than (1,1). The point (1,1) is just an example used for explanation purposes. The slope of 1 can be at any point on the graph where there is a family of curves.
To find the equation of a specific curve in a family of curves with a slope of 1 at (1,1), you can first identify the y-intercept of the desired curve. Then, using the slope-intercept form, you can plug in the slope of 1 and the y-intercept to find the equation of that particular curve.