Question

If the coordinates of point A are (8 , 0) and the coordinates of point B are (3 , 7), the y-intercept of is

Answer 1

As a fraction:
`y=(56)/(5)`

As a decimal:
`y=11.2`

As an ordered pair:
`(0,(56)/(5) )` or
`(0,11.2)`

Explanation:

First we are using the slope formula to find the equation of our line:

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

Where

`m` is the slope of the line

`(x_1,y_1)` are the coordinates of the first point

`(x_2,y_2)` are the coordinates of the second point

our first point is (8, 0) and our second point is (3, 7), so
`x_1=8`,
`y_1=0`,
`x_2=3`, and
`y_2=7`.

Replacing values:

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

`m=(7-0)/(3-8)`

`m=(7)/(-5)`

`m=-(7)/(5)`

Now, to complete the equation of our line (and find its y-intercept), we are using the point slope formula:

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

Where

`m` is the slope

`(x_1,y_1)` are the coordinates of the first point

Replacing values:

`y-0=-(7)/(5) (x-8)`

`y=-(7)/(5) x+(56)/(5)`

Now, in a line of the form
`y=mx+b`,
`b` is the way intercept. We can infer form our line that
`b=(56)/(5)`, so the y-intercept of the line joining the points (8, 0) and (3, 7) is
`(56)/(5)`.