Question

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

Answer 1

Answer:

x intercept is (45/2,0)

y intercept is (0,-36)

Step-by-step 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)

$slope = \frac{y_2-y_1}{x_2-x_1} =\frac{12-20}{15- 10} = \frac{-8}{5}$

m = -8/5

now we find out b using (10,20)

$20 = \frac{-8}{5} (10)+b$

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 $y = \frac{-8}{5}x+36$

To find x intercept plug in 0 for y

$0= \frac{-8}{5}x+36$

subtract 36 on both sides

$-36= \frac{-8}{5}x$

Multiply by -5/8 on both sides

$-36*\frac{-5}{8}=x$

$\frac{45}{2}=x$

x intercept is (45/2,0)