# How do you find the equation of the line that passes through (5, -3), in Standard Form, and is parallel to the line that passes through (4, -5) and (-1, -6)?

##### 1 Answer

#### Explanation:

You know that you must find the equation of a line that passes through point **parralel** to another line that passes through two points,

The important thing to realize here is that two **parralel lines** have the *same slope*, but different

This means that you can use the two points given for the second line to determine its slope, which will be equal to the slope of the target line.

For a general form line that passes through two points

#color(blue)("slope" = m = (y_2 - y_1)/(x_2 - x_1))#

The slope of the *two lines* will be

#m = (-6 - (-5))/(-1 - 4) = ((-1))/((-5)) = 1/5#

You now have the slope of the target line, which means that you can use the point

#color(blue)(y - y_1 = m * (x - x_1))#

#y - (-3) = 1/5 * (x - 5)#

#y + 3 = 1/5(x-5)#

The standard form of a line is

#color(blue)(Ax + By = C)#

Rearrange your equation to get

#y = 1/5x - 1 - 3#

#-1/5x + y = -4" "# #<=># #" "-x + 5y = -20#