Question

Determine the intercepts of the line that passes through the following points.

(6,−3)



(10,−6)




(14,−9)

Answer 1

x-intercept is 2

y-intercept is
`(3)/(2)`

Explanation:

We can select any two points and find equation of line

(6,-3)

so,
`x_1=6,y_1=-3`

(10,-6)

so,
`x_2=10,y_2=-6`

Firstly, we will find slope

`m=(y_2-y_1)/(x_2-x_1)`

now, we can plug values

`m=(-6+3)/(10-6)`

`m=-(3)/(4)`

now, we can point slope form of line

`y-y_1=m(x-x_1)`

we can plug values

`y+3=-(3)/(4)(x-6)`

now, we can solve for y

`y=-(3)/(4)x+(3)/(2)`

x-intercept:

we can set y=0

and then we can solve for x

`0=-(3)/(4)x+(3)/(2)`

`-(3)/(4)x=-(3)/(2)`

`3x=6`

`x=2`

y-intercept:

we can plug x=0

`y=-(3)/(4)* 0+(3)/(2)`

`y=0+(3)/(2)`

we get

`y=(3)/(2)`

So,

x-intercept is 2

y-intercept is
`(3)/(2)`