How to find linear function from two points?

Question:

The graph of a linear function passes the point A (-1, 2) and point B (3, -1). Find the analytical expression of the linear function.

Solution:

The analytical expression of a linear function is y = kx + b, in which k is the slope and b is the y-intercept. Because point A (-1, 2) and point B (3, -1) lie on the graph, so, points A and B satisfy the linear function. Substitute the point A (-1, 2) in to the linear function y = kx + b.

2 = -k + b ... name this asequation1

Substitute the point B (3, -1) in to the linear function y = kx + b

-1 = 3k + b ... name this as equation2

Using equation1 subtract equation2 to remove variable b

2 - (-1) = -k - 3k

2 + 1 = -4k

k = -3/4

substitute the value of k into equation1

2 = - (-3/4) + b

2 = 3/4 + b

b = 2 - 3/4

= 8/4 - 3/4

= 5/4

Therefore, the linear function is y = - (3/4) x + 5/4. Watch the video for more details.