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

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)

Answer 2

Answer:  $(0,34)$

Step-by-step 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:

$m=\frac{y_2-y_1}{x_2-x_1}$

We can say that:

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

Then:

$m=\frac{50-66}{-28-(-56)}=-\frac{4}{7}$

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

$66=-\frac{4}{7}(-56)+b\\\\66-32=b\\\\b=34$

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

$(0,34)$