Question

Determine the intercepts of the line that passes through the following points (10,20) (15,12) (20,4)

Answer 1

x intercept is (45/2,0)

y intercept is (0,-36)

Explanation:

Slope intercept form of equation of line is

y=mx+b where m is the slope and b is the y intercept

use any two points to find the slope

(10,20) (15,12)

`slope = (y_2-y_1)/(x_2-x_1) =(12-20)/(15- 10) = (-8)/(5)`

m = -8/5

now we find out b using (10,20)

`20 = (-8)/(5) (10)+b`

20 = -16 + b

add 16 on both sides , so b = 36

b is the y intercept , so y intercept is (0,-36)

Now we find x intercept

equation of line is y=mx+b that is
`y = (-8)/(5)x+36`

To find x intercept plug in 0 for y

`0= (-8)/(5)x+36`

subtract 36 on both sides

`-36= (-8)/(5)x`

Multiply by -5/8 on both sides

`-36*(-5)/(8)=x`

`(45)/(2)=x`

x intercept is (45/2,0)