what is the equation of the line that is parallel to the given line and passes through the point (12…

what is the equation of the line that is parallel to the given line and passes through the point (12, -2)?\n$y = -\\frac{6}{5}x + 10$\n$y = -\\frac{6}{5}x + 12$\n$y = -\\frac{5}{6}x - 10$\n$y = \\frac{5}{6}x - 12$

what is the equation of the line that is parallel to the given line and passes through the point (12, -2)?\n$y = -\\frac{6}{5}x + 10$\n$y = -\\frac{6}{5}x + 12$\n$y = -\\frac{5}{6}x - 10$\n$y = \\frac{5}{6}x - 12$

Answer

Explanation:

Step1: Find the slope of the given line

The formula for slope (m=\frac{y_2 - y_1}{x_2 - x_1}). Using the points ((0,-4)) and ((12,6)), we have (m=\frac{6-(-4)}{12 - 0}=\frac{10}{12}=\frac{5}{6}). Parallel lines have the same slope.

Step2: Use the point - slope form

The point - slope form is (y - y_1=m(x - x_1)). Substituting (m = \frac{5}{6}), (x_1=12), and (y_1=-2), we get (y-(-2)=\frac{5}{6}(x - 12)).

Step3: Simplify the equation

[ \begin{align*} y + 2&=\frac{5}{6}x-10\ y&=\frac{5}{6}x-12 \end{align*} ]

Answer:

(y = \frac{5}{6}x - 12) (the fourth option)