Question

The table shows a linear function.

Which equation represents the function?

x f(x)
10 −1
5 2
0 5
−5 8

A)f(x)=−53x+5

B)f(x)=−35x+5

C)f(x)=53x+5

D)f(x)=53x−1

Answer 1

B) f(x) = -3/5x +5

Explanation:

There are several ways you can write the equation of a line from a list of points. When you look through the list and see that one of them is the y-intercept, then the problem can be easier. When you look through the list of answers and see that the required answer is in slope-intercept form, then you know all you need to do is find the slope to go with the intercept you've located.

The point (x, f(x)) = (0, 5) tells you the y-intercept is 5.

The slope, the change in y divided by the change in x for two points, is ...

... (-1 -2)/(10 -5) = -3/5

This is the slope and the coefficient of x in the linear equation.

Now, we know the y-intercept (b=5) and the slope (m=-3/5), so we can fill in the slope-intercept form of the equation of a line:

... y = mx + b

... y = (-3/5)x + 5