 Hi, and welcome to the session. Let us discuss the following question. The question says, find the equation of the line perpendicular to the line x minus 7 by plus 5 is equal to 0 and having x intercept 3. Let's now begin with the solution. In this question, we have to find the equation of line which is perpendicular to the line x minus 7 by plus 5 is equal to 0. We know that product or slope of two perpendicular lines is minus 1. We can determine the slope of this given line. So after finding the slope of this given line, we can easily determine the slope of the required line. And since the required line has x intercept 3, therefore it will definitely pass through the point 3, 0. Then finally, we will substitute the value of slope and the point in the equation y minus 5 is equal to m into x minus x y. So let's first find the slope of the given line. Now given line is x minus 7 by plus 5 is equal to 0. This implies minus 7 by is equal to minus x plus 5. This implies 7 by is equal to x plus 5. This implies y is equal to 1 by 7 into x plus 5 by 7. Let's name this equation as equation number 1. On comparing 1 with y is equal to mx plus c, we find that slope that is m is equal to 1 by 7. Since the required line is perpendicular to the given line x minus 7 by plus 5 is equal to 0, therefore product of slopes of these two lines is minus 1. Let m1 be the slope of required line. Now we have m1 into 1 by 7 is equal to minus 5. This implies m1 is equal to minus 7. So the slope of required line is minus 7. Now since the required line intersects 3, required line passes through point b0, we know that equation of line passing through point x1 by 1 and having slope n is pi minus pi 1 is equal to m into x minus x1. Now here the required line passes through the point 3,0. So this means x1 by 1 is equal to 3,0 and slope is minus 7. So now we will substitute the value of x1 by 1 and slope in this equation. Substituting the values we get y minus 0 is equal to minus 7 into x minus 3. This implies y is equal to minus 7x plus 21. This implies y plus 7x is equal to 21. Hence the required equation of line is y plus 7x is equal to 21. This is our required answer. So this completes the session. Bye and take care.