what equations are in the form of y=c+d(x-1)
The equation you mentioned, y = c + d(x-1), represents a linear equation in slope-intercept form, where c and d are constants. In this form, the equation represents a line on a graph.
To understand this equation better, let's break it down:
- "y" represents the dependent variable, or the output of the equation, commonly represented on the vertical axis of a graph.
- "x" represents the independent variable, or the input of the equation, typically represented on the horizontal axis of a graph.
- "c" represents the y-intercept, which is the value of y when x is 0. It determines where the line intersects the y-axis.
- "(x-1)" represents the change in x from the point (1,0), which means the line is shifted horizontally by 1 unit to the right.
- "d" represents the slope of the line, which determines how steep or flat it is. It is the coefficient of the x-term.
To find specific equations in this form, you can substitute different values for c and d. For example:
- y = 2 + 3(x-1)
- y = -1 + 0.5(x-1)
- y = 7 + 2.5(x-1)
By plugging in different values for c and d, you can generate a variety of equations in the specified form.