Determine the Equation of a Line that Passes through a Given Point and is Parallel to another Line Described by another Equation

 Write an equation passing through a given point (-2,-2) parallel to the line given by the equation: y=-1/5 x+9 Solution

To find the equation of a line parallel to a given line, we first need to identify the slope of the given line. The equation of the given line is:

$�=-\frac{1}{5}�+9$

The slope of this line is $-\frac{1}{5}$. Since parallel lines have the same slope, the slope of the line we are trying to find will also be $-\frac{1}{5}$.

Next, we use the point-slope form of a line to find the equation of our line. The point-slope form is:

$�-{�}_1=�(�-{�}_1)$

where $({�}_1,{�}_1)$ is a point on the line and $�$ is the slope. Plugging in the given point $(-2,-2)$ and the slope $-\frac{1}{5}$, we get:

$�-(-2)=-\frac{1}{5}(�-(-2))$ $�+2=-\frac{1}{5}(�+2)$ $�+2=-\frac{1}{5}�-\frac{2}{5}$

Finally, we can rearrange this equation to get it in the standard form:

$�=-\frac{1}{5}�-\frac{2}{5}-2$ $�=-\frac{1}{5}�-\frac{12}{5}$

So, the equation of the line passing through the point $(-2,-2)$ and parallel to the line $�=-\frac{1}{5}�+9$ is:

$�=-\frac{1}{5}�-\frac{12}{5}$