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

Option 2 and option 4 are linear equations.

Step-by-step explanation:

We know the linear equation of the form

where m is the slope and b is the y-intercept.

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

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

simplifying to write in the form y=mx+b

8y-2y = 7x-4

6y = 7x-4

y = 7/6x - 2/3

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

Option 3)

Given the equation

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

Option 4)

Given the equation

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.

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

given : the shape of his satellite can be modeled by   where x and y are modeled in inches.

now,the given equation   is a equation of parabola.

here, coefficient of x is positive, hence the parabola opens rightwards.

on comparing this equation with standard equation , we get

in standard equation, coordinates of focus=(0,m)

thus for given equation coordinates of focus=(0,1.5)

step-by-step explanation: