What is an equation of the line that passes through the points ( 5 , − 6 ) (5,−6) and ( − 5 , − 4 ) (−5,−4)?

Answer 1

The equation of a line can be written in slope intercept form:

y = mx + b where m is the slope and b is the y-intercept

You can use the two points to find the slope m:

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

Now you can select either point and substitute the coordinates in the equation Let's us (5, -6):

y-y₁= m (x + x₁)

y-(-6)=-1/5 (x-5)

y+6=-x/5+1

y=-x/5+1-6

y=-x/5-5

Answer 2

x+5y +25 = 0

(5)+5(-6)+25 = 0

5-30+25 = 0

0 =0

-5 +5(-4) + 25 = 0

-25 +25 = 0

0 = 0

slope of the line through the points = the difference in y coordinates divided by the difference in x coordinates = "rise over run" = (-6- -4)/(5- -5) = (-6+4)/(5+5) = -2/10

= -1/5 = (y+4)/(x+5)

cross multiply to get

5y +20 = -x -5

x+5y +25 = 0 in general form

or

y = (-1/5)x - 5 in slope intercept form