Question

question
what is an equation of the line that passes through the points (0, -6) and (6, 2)?

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0, -6)$ (where $x_1 = 0, y_1 = -6$) and $(6, 2)$ (where $x_2 = 6, y_2 = 2$), we substitute:
$m = \frac{2 - (-6)}{6 - 0} = \frac{2 + 6}{6} = \frac{8}{6} = \frac{4}{3}$

Step2: Identify the y-intercept (b)

The y-intercept is the value of y when $x = 0$. From the point $(0, -6)$, we see that when $x = 0$, $y = -6$. So, $b = -6$.

Step3: Write the equation in slope-intercept form ($y = mx + b$)

Substitute $m = \frac{4}{3}$ and $b = -6$ into the formula:
$y = \frac{4}{3}x - 6$

Answer:

$y = \frac{4}{3}x - 6$