Question

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

Answer 1

Option 2 and option 4 are linear equations.

Explanation:

We know the linear equation of the form

`y=mx+b`

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 equation

• x+1/y = 7

The given equation is a non-linear equation because the exponent of the variable y is -1. i.e. y⁻¹.

Option 2)

Given the equation

• 7x-8y=4-2y

simplifying to write in the form y=mx+b

8y-2y = 7x-4

6y = 7x-4

y = 7/6x - 2/3

• m = 7/6, b = -2/3

Thus, 7x-8y=4-2y is a linear equation

Option 3)

Given the equation

• 2x-3xy+5y = 1

Please note that the term involving xy has degree two. Thus, it is not a linear equation.

Option 4)

Given the equation

• y+1/5x=3

simplifying to write in the form y=mx+b

y = -1/5x+3

m = -1/5, b=3

Thus, y+1/5x=3 is a linear equation.

Thus, option 2 and option 4 are linear equations.