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Find the gradients of the following lines and state whether the lines are constant, increasing or decreasing functions:
ScanSolve AI Answer
Step-by-step solution
7 stepsCalculate the gradient for 10.1.
We use the points and .
The gradient formula is .Since the gradient is positive, the function is increasing.
The gradient for 10.1 is , and it is an increasing function.Calculate the gradient for 10.2.
We use the points and .
Since the gradient is zero, the function is constant.
The gradient for 10.2 is , and it is a constant function.Calculate the gradient for 10.3.
We use the points and .
Since the gradient is negative, the function is decreasing.
The gradient for 10.3 is , and it is a decreasing function.Determine the equation for line g in 11.1.
We use the points and .
First, calculate the gradient:The y-intercept is (from the point ).
Using the slope-intercept form :The equation for line g is .
Determine the equation for line h in 11.1.
Line h is a horizontal line passing through .
The equation for line h is .Determine the equation for 11.2.
We use the points and .
First, calculate the gradient:The y-intercept is (from the point ).
Using the slope-intercept form :The equation for 11.2 is .
Determine the equation for 11.3.
We use the points and .
First, calculate the gradient:The y-intercept is (from the point ).
Using the slope-intercept form :The equation for 11.3 is .
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