This equation is in 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
The slope of an equation in standard form is: m = -color(red)(A)/color(blue)(B)
x - y = 6 is:
color(red)(1)x + color(blue)(-1)y = color(green)(6)
Therefore the slope is: m = color(red)(-1)/color(blue)(-1) = 1
To find the y intercept, set x to 0 and solve for y:
x - y = 6 becomes:
0 - y = 6
-y = 6
color(red)(-1) * -y = color(red)(-1) * 6
y = -6
Therefore, the y-intercept is: -6 or (0, -6)
If you also need the x intercept, do the opposite. Set y to 0 and solve the x:
x - y = 6 becomes:
x - 0 = 6
x = 6
Therefore, the x-intercept is: 6 or (6, 0)
