Come up with a new linear function that has a slope that falls in the range -1<m<0.
I don't really understand how to find this out. Can someone lead me in the right direction please?
You should know that linear functions can be written in the form y = mx + b , (the y-intercept form), except vertical lines which have the form x = c
so let's pick any slope from -1 to 0. How about m = -1/4
Equations with such a slope are
y = (-1/4)x + 7
or
y = (-1/4)x + 3.2575
or
y = (-1/4)x - 5/6
etc
To come up with a linear function that has a slope in the range -1 < m < 0, we need to define the function using the slope-intercept form, which is y = mx + b. In this form, m represents the slope and b represents the y-intercept.
Since we want a slope between -1 and 0, we can choose any value for b and then select a suitable value for m.
Here's a step-by-step process to find a linear function with the desired slope range:
1. Choose a value for the y-intercept, b. For simplicity, let's select b = 0, which means the function will pass through the origin (0, 0).
2. Next, select a value for the slope, m, such that -1 < m < 0. Let's select m = -0.5 as an example.
3. Plug the values of m and b into the slope-intercept form. We get y = -0.5x + 0.
As a result, the linear function y = -0.5x is an example of a linear function with a slope that falls in the range -1 < m < 0.
You can verify the slope of this function by examining the coefficient of x, which is -0.5. Since this value is between -1 and 0, it satisfies the given slope range.