Can someone please help me come up with a linear function that falls in the range -1< m < 0?
can my "m" or slope equal -0.2, -1/3, etc.?
Yes it can be whatever you want between that given range. For example, if the slope was -0.2, (or -1/5) then, your line would go down from left to right (because it's negative) and move down 1 every time you move 5 to the right (m= rise/run)
Hope that helps!
Yes that does help, thank you so much.
Sure! In order to come up with a linear function that falls in the range -1 < m < 0, we need to consider the slope of the line. The slope, denoted by m, determines the steepness or slope of the line.
To create a linear function falling in this range, we can use a negative slope, where -1 < m < 0. This means that the line will have a downward or negative direction from left to right, but it won't be too steep.
Let's start by using a simple form of a linear function: y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope, and b represents the y-intercept (where the line crosses the y-axis).
To meet the criteria of -1 < m < 0, we can choose a value for m that is within this range. For example, let's choose m = -0.5.
With m = -0.5, our linear function becomes: y = -0.5x + b
To determine the value of b (the y-intercept), we can choose any value for x and y and substitute it into the equation. For simplicity, let's choose x = 0. When x = 0, the equation becomes y = -0.5(0) + b, which simplifies to y = b.
Since we want a linear function falling below the x-axis (the range -1 < m < 0), we need to set b to be a negative value. For example, let's set b = -2.
Substituting the values into the equation, we get y = -0.5x - 2 as our linear function falling in the desired range.
You can test different values for x in this equation and calculate the corresponding y-values to plot the line and confirm that it falls in the range -1 < m < 0.