Question

on of the line described. through (18, - 2, - 5), parallel to y = 2 - x/7 - 3

Explanation:

Step1: Identify slope of given line

The given line is $y=\frac{2}{7}x - 3$, its slope $m_1=\frac{2}{7}$. Parallel lines have equal slopes, so the slope of the new line $m = \frac{2}{7}$.

Step2: Use point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. We have the point $(x_1,y_1)=(-2,-5)$ and $m=\frac{2}{7}$. Substitute these values: $y-(-5)=\frac{2}{7}(x - (-2))$.

Step3: Simplify the equation

$y + 5=\frac{2}{7}(x + 2)$. Expand the right - hand side: $y+5=\frac{2}{7}x+\frac{4}{7}$. Then subtract 5 from both sides: $y=\frac{2}{7}x+\frac{4}{7}-5$. Since $5=\frac{35}{7}$, we get $y=\frac{2}{7}x+\frac{4 - 35}{7}$, so $y=\frac{2}{7}x-\frac{31}{7}$.

Answer:

$y=\frac{2}{7}x-\frac{31}{7}$