Question

unit 8: algebraic connections to geometry - copy
if line g contains points (3,5) and (7,-3), determine the equation of the line parallel to line g passing through point (-2,6).
○ y = \frac{1}{2}x + 7
○ y = \frac{1}{2}x + 5
○ y = -2x + 2
○ y = -2x + 10

Explanation:

Step1: Calculate the slope of line \(g\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Given points \((x_1,y_1)=(3,5)\) and \((x_2,y_2)=(7, - 3)\), then \(m=\frac{-3 - 5}{7 - 3}=\frac{-8}{4}=-2\).
Since parallel lines have the same slope, the slope of the new line is also \(m=-2\).

Step2: Use the point - slope form \(y - y_0=m(x - x_0)\)

The point - slope form of a line is \(y - y_0=m(x - x_0)\), where \((x_0,y_0)=(-2,6)\) and \(m=-2\).
Substitute the values: \(y - 6=-2(x+2)\).

Step3: Simplify the equation

Expand the right - hand side: \(y - 6=-2x-4\).
Add 6 to both sides: \(y=-2x + 2\).

Answer:

\(y=-2x + 2\) (the third option)