Write a linear function f with f(−3)=1 and f(13)=5.

Answer 1

Hi Quaronna,

We have to sets of points: (-3,1) and (13,5) that are on the same line. The first thing to do is we can find the slope of the line. To do this, we can use the equation m= (y2-y1(/(x2-x1).

Let's plug in our data points to our slope equation. m =(5-1)/(13-(-3)). This gives us a slope of 1/4. The start of our equation is f(x)=y=1/4x+b.

Let's plug in one of our data points into the slope intercept form to identify b. We can use (-3,1) for this. So we get 1=1/4(-3)+b. When we solve for b, we get 7/4.

Our linear function is now f(x)=1/4x+7/4. We can validate this by plugging in the x of the other data point and we should expect to have the same output y.

f(x)=1/4(13)+7/4=13/4+7/4=20/4=5 The data point matches.

Ultimate linear function=f(x)=1/4x+7/4