Question

This table gives a few (x,y) pairs of a line in the coordinate plane.

what is the y intercept of the line?

Answer 1

y = -23

Explanation:

Equation of line in intercept form is y = mx + c

Where m = slope of the line

and c = y-intercept

Now slope m =
`((y-y')/(x-x') )` where (x, y) and (x',y') are the points lying on the line

If two points are (-72, 25) and (-54, 113)

so m =
`((25-13)/(-72-54) )`

=
`((-12)/(18)` =
`((-2))/(3) )`

Now equation of the line will be y =
`((-2)/(3)x+c`

This line passes through (-36, 1)

So 1 =
`((-2))/(3) )` × (-36) + c

1 = 2 × (+12) + c

1 + +24 + c ⇒ c = 1 -24

= -23

Answer 2

y intercept is -23

Explanation:

Here we are given three coordinates and are asked to find y intercept of the line passing through these points.

We thus find the equation of this line by two point form

the form says

(y-y1)/(x-x1) = (y2-y1)/(x2-x1)

Here (x1,y1) = ( -36 , 1 )

and (x2,y2) = ( 13,-54)

Substituting the values we get

(y-1)(x+36)=(1-13)/(-36-(-54))

(y-1)(x+36)=(-12)/(-36+54)

(y-1)(x+36)=(-12)/(18)

y-1=-2/3 ( x+36)

In order to determine the y intercept we are required to leep x = 0 in above equation and solve for y

y-1 = -2/3 (0+36 )

y-1= (-2/3) x (36 )

y-1 = -2 x 12

y-1 = -24

adding 1 on both hand sides

y = -24 +1

y=-23