Determine which equations are linear. (check all that apply)

Answer:Option 2 and option 4 are linear equations.Step-by-step explanation:We know the linear equation of the form[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.The graph of y=mx+b is a straight line.We also need to check that the equation must not have any exponent. In other words, the degree of a linear equation must be 1.Let us check whether the given equations are linear or not.Option 1)Given the equationx+1/y = 7The given equation is a non-linear equation because the exponent of the variable y is -1. i.e. y⁻¹.Option 2)Given the equation7x-8y=4-2ysimplifying to write in the form y=mx+b8y-2y = 7x-46y = 7x-4y = 7/6x - 2/3m = 7/6, b = -2/3Thus, 7x-8y=4-2y is a linear equationOption 3)Given the equation2x-3xy+5y = 1Please note that the term involving xy has degree two. Thus, it is not a linear equation.Option 4)Given the equationy+1/5x=3simplifying to write in the form y=mx+by = -1/5x+3m = -1/5, b=3Thus, y+1/5x=3 is a linear equation.Thus, option 2 and option 4 are linear equations.