Someone please help, its for a hw assignment I have due today. What is the equation of the line through (3, 7) that is perpendicular to the line through points (-1, -2) and (5, 3)?

The required equation is:[tex]y=-\frac{6}{5}x+\frac{53}{5}[/tex]Step-by-step explanation:Let l_1 be the line through  (-1, -2) and (5, 3)and l_2 be the line we require which passes through (3,7)We have to find the lope of l_1 first[tex]m_1=\frac{y_2-y_1}{x_2-x_1}\\=\frac{3-(-2)}{5-(-1)}\\=\frac{3+2}{5+1}\\=\frac{5}{6}[/tex]we have to find the equation of line perpendicular to l1The product of slopes of two perpendicular lines is -1Let m_2 be the slope of l_2Then[tex]\frac{5}{6}*m_2=-1\\m_2=-\frac{6}{5}[/tex]The general slope-intercept form is:y=mx+bPutting the value of slope[tex]y=-\frac{6}{5}x+b[/tex]To find the value of b, we will put (3,7) in the equation[tex]7=-\frac{6}{5}(3)+b\\7=-\frac{18}{5}+b\\b=7+\frac{18}{5}\\b=\frac{35+18}{5}\\b=\frac{53}{5}[/tex]Putting the values of b and m in standard slope intercept form:[tex]y=-\frac{6}{5}x+\frac{53}{5}[/tex]Hence,The required equation is:[tex]y=-\frac{6}{5}x+\frac{53}{5}[/tex]Keywords: Equation of lineLearn more about equation of line at:brainly.com/question/702593brainly.com/question/7128279#LearnwithBrainly