Find an equation for the line parallel to the line −14x−7y=−4 having the same y-intercept as 4x−3y=−6

Answer 1

To determine the slope and y intercept, need to put both equations in the form y=mx+b

Equation 1:

-14x-7y=-4

Add 14x to both sides

-14x-7y+14x=-4+14x

Simplify

-7y=14x-4

Divide both side by -7

-7y/-7=14x/-7-4/-7

Simplify

y=-2x+4/7 If the slope of this line is -2, the slope of a line parallel to this is also -2, so m=-2

Equation 2

4x-3y=-6

Subtract 4x from both sides

4x-3y-4x=-6-4x

Simplify

-3y=-4x-6

Divide both sides by -3

-3y/-3=-4x/-3-6/-3

Simplify

y=4/3x+2 The y intercept is 2, so b=2

Bringing those 2 values together, the equation is:

y=-2x+2