Question

do you know how?
use the diagram for exercises 6 - 9.

1. are lines g and n parallel? no
2. are lines j and m parallel? yes
3. are lines n and k perpendicular?
4. are lines h and j perpendicular?
5. what is an equation for the line parallel to ( y = -x + 7 ) that passes through ( (7,-2) )?
6. what is an equation for the line perpendicular to ( y = 3x - 1 ) that passes through ( (-9,-2) )?
7. the graph of a roller - coaster track goes in a straight line through coordinates ( (10,54) ) and ( (42,48) ), with coordinates in feet. a support beam runs parallel 12 feet below the track. what equation describes the support beam?

Explanation:

Step1: Find the slope of the given line

The equation of a line is \(y = mx + b\), where \(m\) is the slope. For the line \(y=-x + 7\), the slope \(m=-1\). Parallel lines have the same slope. So the slope of the line we want to find is also \(m=-1\).

Step2: Use the point - slope form

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)\) is a point on the line. We have \(m=-1\) and the point \((7,-2)\), so \(x_1 = 7\) and \(y_1=-2\).
Substitute into the formula: \(y-(-2)=-1(x - 7)\)

Step3: Simplify the equation

\(y + 2=-x + 7\)
Subtract 2 from both sides: \(y=-x+7 - 2\)
\(y=-x + 5\)

Answer:

\(y=-x + 5\)