which line is perpendicular to the line whose equation is 5y+6=-3x?

1) y= -5/3+7
2) y= 5/3+7
3) y= -3/5+7
4) y= 3/5+7

To find the line that is perpendicular to the given line, you need to determine the slope of the given line and then find the negative reciprocal of that slope.

The given line equation is 5y + 6 = -3x. To put it in slope-intercept form (y = mx + b), you need to isolate y. Start by subtracting 6 from both sides:

5y = -3x - 6

Divide both sides of the equation by 5 to solve for y:

y = -3/5x - 6/5

The slope of this line is -3/5.

The slope of a line perpendicular to this line will be the negative reciprocal of -3/5. To find the negative reciprocal, you flip the fraction and change the sign. The negative reciprocal of -3/5 is 5/3.

Now that you have the slope of the perpendicular line, you can check which of the given options has a line with a slope of 5/3.

Let's examine each option by comparing the slope-intercept form (y = mx + b):

1) y = -5/3 + 7: The slope is -5/3, not 5/3.
2) y = 5/3 + 7: The slope is 5/3, which matches the perpendicular slope.
3) y = -3/5 + 7: The slope is -3/5, not 5/3.
4) y = 3/5 + 7: The slope is 3/5, not 5/3.

Therefore, option 2) y = 5/3 + 7 is the line that is perpendicular to the given line.