Question

write the equation of a line that is parallel to (y = -\frac{3}{2}x - 1) and that passes through the point ((4,6)).

Explanation:

Step1: Identify the slope

Parallel lines have the same slope. The slope of the line $y =-\frac{3}{2}x - 1$ is $m =-\frac{3}{2}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(4,6)$ and $m =-\frac{3}{2}$. Substitute the values: $y - 6=-\frac{3}{2}(x - 4)$.

Step3: Simplify the equation

Expand the right - hand side: $y - 6=-\frac{3}{2}x+6$. Then add 6 to both sides to get the slope - intercept form. $y=-\frac{3}{2}x + 12$.

Answer:

$y=-\frac{3}{2}x + 12$