Yes. y + x = 4 is a linear function because the highest order (exponent) on any dependent or independent variable is 1. So if it were y^2 + x = 4 or y + x^3 = 4 or yx + 4 = 0 or anything like that, it would be non-linear. If that doesn't help, if you rearrange y + x = 4 into standard y = mx + b format you get y = -x + 4. So it's a straight line with a slope of -1 and y-intercept of 4. Any time you have an equation that just has the letters in it (x, y, z, etc. any letter) without any exponents, it's a linear equation.
y=x+4
It is a linear equation in one variable, p.
It is linear. The highest power is 1 (x = x1, y = y1) so it is linear.
Two equations: a linear one in y and a quadratic in x.
Yes.
5xy+4=9
y=x+4
It is a linear equation in the variable z.
colinear and non-colinear are terms that are used when describing points in space, not the graph of a function. Maybe what you meant is "Is the function linear?" The answer to that question is no.
Yes, a linear equation in t.
No, it is not.No, it is not.
It is a linear equation in one variable, p.
It is linear. The highest power is 1 (x = x1, y = y1) so it is linear.
Two equations: a linear one in y and a quadratic in x.
Yes.
Yes.
Yes, 2y = 8 is a linear function. 2y = 8 is the same as y=8/2, or y=4, which is a vertical line.