Question

Which equation is parallel to the line LaTeX: y=\frac{1}{2}x+3y = 1 2 x + 3and passes through the point (10, -5)?

Answer 1

Answer:

$Equation\ of\ line:\ y=\frac{1}{2}x-10$

Step-by-step explanation:

$Let\ the\ required\ equation\ is\ y=mx+c\\\\where\ m\ is\ the\ slope\ of\ the\ equation\ and\ c\ is\ y-intercept\\\\It\ is\ parallel\ to\ the\ equation\ y=\frac{1}{2}x+3\\\\Hence\ slope\ of\ these\ two\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{2}x+3\ is\ \frac{1}{2}\\\\Hence\ slope\ of\ y=mx+c\ is\ \frac{1}{2}\Rightarrow m=\frac{1}{2}\\\\Equation:y=\frac{1}{2}x+c\\\\Line\ passes\ through\ (10,-5).\ Hence\ this\ point\ satisfies\ the\ equation\ of\ line.\\\\-5=\frac{1}{2}\times 10+c$

$-5=-5+c\\\\c=-10$

$Equation\ of\ line:\ y=\frac{1}{2}x-10$