How do you find a standard form equation for the line with (-1,3) and parallel to the line 3x+5y=15?

First, we need to find the slope of the line. The equation in the problem is Standard Linear form. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#

Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.

#color(red)(3)x + color(blue)(5)y = color(green)(15)#

The slope of an equation in standard form is: #m = -color(red)(A)/color(blue)(B)#

Therefore, the slope of this line is:

#m = -color(red)(3)/color(blue)(5)#

Because the problem is to find the equation of a parallel line, the slope of the line in the problem will be the same as the slope of the equation for the solution. We can then substitute this slope into the formula to give:

#color(red)(3)x + color(blue)(5)y = color(green)(C)#

We have a point given in the problem. We can take the values from this point, substitute them for #x# and #y# to calculate #color(green)(C)#:

#color(red)(3)x + color(blue)(5)y = color(green)(C)# becomes:

#(color(red)(3) xx -1) + (color(blue)(5) xx 3) = color(green)(C)#

#-3 + 15 = color(green)(C)#

#12 = color(green)(C)#

Substituting this solution for #color(green)(C)# into the formula with the slope gives:

#color(red)(3)x + color(blue)(5)y = color(green)(12)#