The change in y is
(-1) - (7) = -8.
The change in x is
(5) - (-3) = +8.
The slope is (change in y)/(change in x), or
slope = (-8)/(+8) = -1.
The standard form equation for a line with a slope of -1 will be
x + y = (some constant)
We can add the coordinates of one of the points to find that (some constant) = 4.
Your line is
x + y = 4 _____
The slope of the standard form line
ax + by = c
is given by
slope = -a/b.
When the slope is -1, it means a=b. The smallest positive integer values for which this can be true are a=b=1, so that the line becomes x+y=c.
(-1) - (7) = -8.
The change in x is
(5) - (-3) = +8.
The slope is (change in y)/(change in x), or
slope = (-8)/(+8) = -1.
The standard form equation for a line with a slope of -1 will be
x + y = (some constant)
We can add the coordinates of one of the points to find that (some constant) = 4.
Your line is
x + y = 4 _____
The slope of the standard form line
ax + by = c
is given by
slope = -a/b.
When the slope is -1, it means a=b. The smallest positive integer values for which this can be true are a=b=1, so that the line becomes x+y=c.