Question

Through (-4,5) and parallel to y = -3/2x-5

Answer 1

**Disclaimer** Hi there! I assumed the question to be asking for a line expression. The following answer will be according to this understanding. Please let me know if I am incorrect and I will modify my answer correspondingly

Answer: $\Large\boxed{y-5=-\dfrac{3}{2} (x+4)}$

Step-by-step explanation:

Given information

$\text{Pass~through~point}=(x_1,~y_1)=(-4,~5)$

$\text{Parallel~to}:y=-\dfrac{3}{2} x-5$

Given equation form

Point-slope form is the most efficient way to write the expression

$\text{Point-slope form}:y-y_1=m(x-x_1)$

$(x_1,~y_1)=\text{A point that the line passes through}$

$m=\text{Slope}$

Determine the slope

$\text{Since the line is parallel to } y=-\dfrac{3}{2} x-5 \text{ , by the property of parallel}\\\text{lines, the slope of the given line is also }-\dfrac{3}{2}$

$\text{Therefore, m}=-\dfrac{3}{2}$

Substitute values into the given form

$y-y_1=m(x-x_1)$

$y-(5)=-\dfrac{3}{2} (x-(-4)$

Simplify the expression

$\Large\boxed{y-5=-\dfrac{3}{2} (x+4)}$

Hope this helps!! :)

Please let me know if you have any questions