Question

this table gives a few $(x,y)$ pairs of a line in the coordinate plane.
$x$ $y$
$-28$ $-54$
$-21$ $-40$
$-14$ $-26$
what is the $y$-intercept of the line?

Explanation:

Step1: Calculate slope $m$

Choose two points $(-28, -54)$ and $(-21, -40)$.
Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
$m = \frac{-40 - (-54)}{-21 - (-28)} = \frac{14}{7} = 2$

Step2: Use point-slope form

Use point $(-14, -26)$ and $m=2$.
Point-slope: $y - y_1 = m(x - x_1)$
$y - (-26) = 2(x - (-14))$
$y + 26 = 2(x + 14)$

Step3: Simplify to slope-intercept form

Expand and isolate $y$:
$y + 26 = 2x + 28$
$y = 2x + 28 - 26$
$y = 2x + 2$

Step4: Identify y-intercept

The y-intercept is the point where $x=0$. Substitute $x=0$:
$y = 2(0) + 2 = 2$
So the point is $(0, 2)$

Answer:

$(0, 2)$