what is the equation of the line that is parallel to the given line and passes through the point (2, 3)?\n○…

Answer:

$x + 2y = 8$

Explanation:

Step1: Calculate the slope of the given line.

The line passes through points $(-4, 0)$ and $(4, -4)$. $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 0}{4 - (-4)} = \frac{-4}{8} = -\frac{1}{2}$$

Step2: Determine the slope of the parallel line.

Parallel lines have the same slope. The slope of the required line is $m = -\frac{1}{2}$.

Step3: Use the point-slope form for the new line.

The line passes through $(2, 3)$ with slope $m = -\frac{1}{2}$. $$y - y_1 = m(x - x_1)$$ $$y - 3 = -\frac{1}{2}(x - 2)$$

Step4: Convert the equation to standard form.

Multiply both sides by 2: $$2(y - 3) = -1(x - 2)$$ $$2y - 6 = -x + 2$$ Rearrange the terms: $$x + 2y = 2 + 6$$ $$x + 2y = 8$$