Question

what is an equation of the line that passes through the points (0, 4) and (-6, 8)?

Explanation:

Step1: Find the slope (m)

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

Step2: Identify the y-intercept (b)

The point $(0, 4)$ is the y-intercept because when $x = 0$, $y = 4$. So $b = 4$.

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

Substitute $m = -\frac{2}{3}$ and $b = 4$ into the formula: $y = -\frac{2}{3}x + 4$.

Answer:

The equation of the line is $y = -\frac{2}{3}x + 4$