Please help!!Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the given equation.

Answer:Step-by-step explanation:10) The equation of a straight line can be represented in the slope-intercept form, y = mx + cWhere c = interceptFor two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The given equation is 4x + 7y = 67y = - 4x + 6y = -4x/7 + 6/7Comparing with the slope intercept form,Slope, m = -4/7This means that the slope of the line that is perpendicular to it is 7/4The given points are (-4,1)To determine c,We will substitute m = 7/4, y = 1 and x = - 4 into the equation, y = mx + c. It becomes1 = 7/4 × -4 + c1 = - 7 + cc = 8The equation becomesy = 7x/4 + 811) 5x + 4y = 8 (10,5)For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The given equation is 5x + 4y = 84y = - 5x + 8y = -5x/4 + 2Comparing with the slope intercept form,Slope, m = -5/4This means that the slope of the line that is perpendicular to it is 4/5The given points are (10,5)To determine c,We will substitute m = 4/5, y = 5 and x = 10 into the equation, y = mx + c. It becomes5 = 4/5 × 10 + c5 = 8 + cc = 5 - 8 = - 3The equation becomesy = 4x/5 - 312) 2x - 5y = - 10 (4 ,-5)For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The given equation is 2x - 5y = -105y = 2x + 10y = 2x/5 + 2Comparing with the slope intercept form,Slope, m = 2/5This means that the slope of the line that is perpendicular to it is - 5/2The given points are (4, -5)To determine c,We will substitute m = - 5/2, y = - 5 and x = 4 into the equation, y = mx + c. It becomes- 5 = - 5/2 × 4 + c- 5 = -10 + cc = - 5 + 10 = 5The equation becomesy = - 5x/2 + 5