What is the equation of a line that passes through the point (10, 5) and is perpendicular to the line whose equation is y=5/4x−2 ?

Answer:[tex]\displaystyle 4x + 5y = 65\:or\:y = -\frac{4}{5}x + 13[/tex]Step-by-step explanation:5 = −⅘[10] + b −8[tex]\displaystyle 13 = b \\ \\ y = -\frac{4}{5}x + 13[/tex]If you want it in Standard Form: y = −⅘x + 13+ ⅘x + ⅘x___________⅘x + y = 13 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]5[⅘x + y = 13][tex]\displaystyle 4x + 5y = 65[/tex]* Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES], so 1¼ [or 5⁄4] becomes −⅘.I am joyous to assist you anytime.