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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.

Q: Is y equals x plus 4 a linear function and why?

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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.

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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.