Find an equation of the line that runs through (-5,-6) parallel to 2x+5y=7 using function notation

Answer 1

2x + 5y = 7

5y = -2x + 7

y = -2x/5 + 7/5 the slope is the coefficient of the x term, when the equation is solved for y

slope = -2/5. Any parallel line also has the same slope

slope is also the difference in y coordinates divided by difference in x coordinates. Do that with two points (-5, -6) and a generic (x,y) point to get:

(y+6)/(x+5) = -2/5

5y +30 = -2x -10

2x +5y + 40 = 0 is the equation of the parallel line through the given point

for "functional notation" you want f(x) = y = -2x/5 - 8

f(x) = -2x/5 -8

or

f(x) = (-2/5)x - 8