a given line has the equation 10x + 2y=-2. what is the equation, in slope - intercept form, of the line that…

Explanation:

Step1: Rewrite given line in slope - intercept form

The slope - intercept form is $y = mx + b$. Given $10x+2y=-2$, solve for $y$: $2y=-10x - 2$, so $y=-5x - 1$. The slope $m$ of the given line is $- 5$.

Step2: Use the slope of parallel lines

Parallel lines have the same slope. So the slope of the new line is also $m=-5$.

Step3: Use the point - slope form to find the equation

The point - slope form is $y - y_1=m(x - x_1)$. The line passes through $(0,12)$, so $x_1 = 0$ and $y_1=12$. Substituting $m=-5$, $x_1 = 0$ and $y_1 = 12$ into the point - slope form: $y-12=-5(x - 0)$.

Step4: Convert to slope - intercept form

Expand $y-12=-5(x - 0)$: $y-12=-5x$, then $y=-5x + 12$.

Answer:

A. $y=-5x + 12$