Write an equation of the line through (5,5)and parallel to the line 4x+3y=-2

First out the equation 4x + 3y = -2 into slope-intercept form (y = mx + b).

4x + 3y = -2

Subtract 4x from both sides.

3y = -4x - 2

Divide all terms by 3.

y = -4/3x - 2/3

The slope in this equation is -4/3 (4 down, 3 to the right).

Using that slope, input the coordinates (5, 5) into the equation of a line:

y - y1 = m(x - x1)

y - 5 = -4/3(x - 5)

y - 5 = -4/3x + 20/3

y = -4/3x + 35/3

The equation of the line is y = -4/3x + 35/3.