Question

Complete the point-slope equation of the line through ( 1, 10) and (5.2).

Use exact numbers.
y
2 =

Answer 1

y = -2x + 12

Explanation:

The point-slope equation for a line has the following format:

y = mx + b

In which m is the slope and b is the y-intercept(value of y when x = 0).

(1,10)

This means that when x = 1, y = 10. So

10 = m + b

(5,2)

This means that when x = 5, y = 2. So

2 = 5m + b

From the first equation, b = 10 - m. So

2 = 5m + 10 - m

2 = 4m + 10

4m = -8

m = -2

And

b = 10 - m = 10 - (-2) = 10 + 2 = 12

So

y = -2x + 12