Final answer:
To find the equation of a line that passes through a given point and is perpendicular to another line, you first need to determine the slope of the given line and then find the negative reciprocal of that slope.
Step-by-step explanation:
The given equation is 5(y+x)-4(x-y)=-6. To find a line that passes through the point (11,13) and is perpendicular to this line, we need to determine the slope of the given line and then find the negative reciprocal of that slope to get the slope of the perpendicular line.
First, let's simplify the given equation: 5y + 5x - 4x + 4y = -6. Combining like terms, we have 9y + x = -6. Rearranging the equation, we get y = (-1/9)x - 6/9. The slope of this line is -1/9.
The slope of a line perpendicular to the given line is the negative reciprocal of -1/9, which is 9. So, the equation of the perpendicular line is y = 9x + b. To find the value of b, we substitute the coordinates of the given point (11,13) in the equation and solve for b. Plugging in the values, we have 13 = 9(11) + b. Solving for b, we get b = -98.
Therefore, the equation of the line that passes through the point (11,13) and is perpendicular to 5(y+x)-4(x-y)=-6 is y = 9x - 98.