what is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (-2…

Explanation:

Step1: Find the slope of the given line

Rewrite $5x + 2y=12$ in slope - intercept form $y = mx + b$ (where $m$ is the slope and $b$ is the y - intercept). $2y=-5x + 12$, so $y=-\frac{5}{2}x+6$. The slope of the given line is $m =-\frac{5}{2}$. Parallel lines have the same slope.

Step2: Use the point - slope form to find the equation of the new line

The point - slope form is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-2,4)$ and $m =-\frac{5}{2}$. $y - 4=-\frac{5}{2}(x+2)$.

Step3: Simplify the equation

$y - 4=-\frac{5}{2}x-5$. Add 4 to both sides: $y=-\frac{5}{2}x-1$.

Answer:

$y =-\frac{5}{2}x - 1$