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

Answer:
`(0,34)`

Explanation:

The equation of the line in Slope-Intercept form is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

Given the table shown in the image, we can find "m" with this formula:

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

We can say that:

`y_2=50\\y_1=66\\\\x_2=-28\\x_1=-56`

Then:

`m=(50-66)/(-28-(-56))=-(4)/(7)`

Finally, you need substitute the slope and any point on the line into
`y=mx+b` and solve for "b":

`66=-(4)/(7)(-56)+b\\\\66-32=b\\\\b=34`

Since the line intersects the y-xis when
`x=0`, then the point is:

`(0,34)`

Answer 2

The Y-intercept is the Y value when X = 0.

Find the change in X:

-56 to -42 = 14

-42 to -28 = 14

The X value changes by 14.

For every change in X the Y change:

66-58 = 8

58-50 = 8

For X to get from -28 to 0 would be 2 more changes:

-28 +14 = -14

-14 + 14 = 0

2 more changes of Y would be:

50-8 = 42

42-8 = 34

So when X = 0, Y = 34

The Y-intercept would be (0,34)