Linear Function y=mx+b - Examples, Exercises and Solutions

Remember that the rate of change equals the slope.

In this function:

$m=-3$

Therefore, the function is decreasing.

Let's remember that the rate of change equals the slope.

In this case, the slope is:

$m=1$

Remember the formula for calculating a slope using points:

Now, replace the data in the formula with our own:

$\frac{(5-1)}{(2-4)}=\frac{4}{-2}=-2$

To solve the problem, remember the formula to find the slope using two points

Now, we replace the given points in the calculation:

 $\frac{(0-2)}{(0-(-8)}=\frac{-2}{8}=-\frac{1}{4}$

Let's start with option A

In a linear function, to check if the functions are parallel, you must verify if their slope is the same.

y = ax+b

The slope is a

In the original formula:

 y = -x+1

The slope is 1

In option A there is no a at all, which means it equals 1, which means the slope is not the same and the option is incorrect.

Option B:

To check if the function passes through the points, we will try to place them in the function:

-1 = -(-2)+1

-1 = 2+1

-1 = 3

The points do not match, and therefore the function does not pass through this point.

Option C:

We rearrange the function, in a way that is more convenient:

y = -1-x

y = -x-1

You can see that the slope in the function is the same as we found for the original function (-1), so this is the solution!

Option D:

When the slope is negative, the function is decreasing, as the slope is -1, the function is negative and this answer is incorrect.