Write an Equation Passing through a Given Point Parallel to a Line Given by an Equation

 Write an equation passing through a given point (-3, 5) parallel to the line given by the equation: y=3/4 x - 4 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:

$�=\frac{3}{4}�-4$

The slope of this line is $\frac{3}{4}$. Since parallel lines have the same slope, the slope of the line we are trying to find will also be $\frac{3}{4}$.

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 $(-3,5)$ and the slope $\frac{3}{4}$, we get:

$�-5=\frac{3}{4}(�-(-3))$ $�-5=\frac{3}{4}(�+3)$ $�-5=\frac{3}{4}�+\frac{9}{4}$

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

$�=\frac{3}{4}�+\frac{9}{4}+5$ $�=\frac{3}{4}�+\frac{29}{4}$

So, the equation of the line passing through the point $(-3,5)$ and parallel to the line $�=\frac{3}{4}�-4$ is:

$�=\frac{3}{4}�+\frac{29}{4}$