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

Answer 1

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.