Question

This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane. -28 -54 -21 -40 -14 -26 What is the y-intercept of the line?

Answer 1

Answer:

The y-intercept is y = 2

Step-by-step explanation:

A linear function has the following format:

$y = mx + b$

In which m is the slope and b is the y-intercept, which is the value of y when x = 0.

We are given these three points:

(-28, -54)

(-21, -40)

(-14, -26)

We use two of them to build a system, to find values for m and b.

(-28, -54)

This means that when $x = -28, y = -54$

So

$y = mx + b$

$-54 = -28m + b$

$28m = b + 54$

$m = \frac{b + 54}{28}$

(-21, -40)

This means that when $x = -21, y = -40$

So

$y = mx + b$

$-40 = -21m + b$

$-40 = -21\frac{b + 54}{28} + b$

$-40 = \frac{-21b - 1134 + 28b}{28}$

$7b - 1134 = -40*28$

$7b = 14$

$b = \frac{14}{7}$

$b = 2$

The y-intercept is y = 2