Question

How to write a linear function (f) with the given values, f(6)=9, f(-5)=0

Answer 1

To write a linear function with the given values, f(6)=9 and f(-5)=0, we need to find the slope (m) and y-intercept (b) of the linear function f(x).

Step 1: Finding the Slope (m)
The slope (m) is determined by the change in y divided by the change in x. In this case, we have two points: (6, 9) and (-5, 0).

Change in y = 9 - 0 = 9
Change in x = 6 - (-5) = 11

So, the slope (m) is 9/11.

Step 2: Finding the y-intercept (b)
We can use one of the given points to find the y-intercept (b). Let's use the point (6, 9).

Using the slope-intercept form of a linear function, which is y = mx + b, we can substitute the values.

9 = (9/11) * 6 + b
9 = (54/11) + b

To isolate b, subtract (54/11) from both sides:

9 - (54/11) = b
(99/11) - (54/11) = b
(99 - 54)/11 = b
45/11 = b

So, the y-intercept (b) is 45/11.

Step 3: Writing the Linear Function
Now that we have the slope (m) and y-intercept (b), we can write the linear function as:

f(x) = (9/11) * x + 45/11

Therefore, the linear function f(x) with the given values is f(x) = (9/11) * x + 45/11.