Question

target: i can identify and write the equations of parallel lines, including horizontal and vertical lines.
the equation ( x = - 3 ) is graphed on the coordinate plane. (use this graph for problems 4 & 5)

1. graph the line perpendicular to ( x = - 3 ) that passes through ( ( 8, - 5 ) ).
2. graph the line parallel to ( x = - 3 ) that passes through ( ( 6, - 2 ) ), then write the equation.
3. write the equation of a line that is perpendicular ( y = - 3 ) but through the point ( ( - 7, - 3 ) ).

Explanation:

Step1: Analyze the nature of \(x = - 3\)

The equation \(x=-3\) represents a vertical line. A line perpendicular to a vertical line is a horizontal line. The equation of a horizontal line is of the form \(y = k\), where \(k\) is the \(y\) - coordinate of any point on the line. Since the line passes through \((8,-5)\), the \(y\) - coordinate is \(-5\). So the equation of the line perpendicular to \(x = - 3\) passing through \((8,-5)\) is \(y=-5\).

Step2: Analyze the nature of \(x = - 3\) for parallel line

The equation \(x=-3\) is a vertical line. A line parallel to a vertical line is also a vertical line. The equation of a vertical line is of the form \(x = h\), where \(h\) is the \(x\) - coordinate of any point on the line. Since the line passes through \((6,-2)\), the \(x\) - coordinate is \(6\). So the equation of the line parallel to \(x=-3\) passing through \((6, - 2)\) is \(x = 6\).

Step3: Analyze the nature of \(y=-3\)

The equation \(y = - 3\) is a horizontal line. A line perpendicular to a horizontal line is a vertical line. The equation of a vertical line is of the form \(x = h\), where \(h\) is the \(x\) - coordinate of any point on the line. Since the line passes through \((-7,-3)\), the \(x\) - coordinate is \(-7\). So the equation of the line perpendicular to \(y=-3\) passing through \((-7,-3)\) is \(x=-7\).

Answer:

1. The equation of the line is \(y = - 5\).
2. The equation of the line is \(x = 6\).
3. The equation of the line is \(x=-7\).