Question

1. fill in the blanks using the available answer choices.

select whether the pair of lines is parallel, perpendicular, or neither.
$x=-2,y = 10$
(blank 1)
blank 1 options

• parallel
• perpendicular
• neither

1. fill in the blanks using the available answer choices.

select whether the pair of lines is parallel, perpendicular, or neither.
$y = 5,y=-3$
(blank 1)
blank 1 options

• parallel
• perpendicular
• neither

1. write an equation in slope - intercept form for the line described.

passes through $(-1,-10)$, parallel to $y = 7$
$y=$

1. podiums a carpenter is building a podium. the side panel of the podium is cut from a rectangular piece of wood.

the rectangle must be sawed along the dashed line in the figure. what is the measure of $\angle1$?

Explanation:

Step1: Analyze the line \(x = - 2\)

The line \(x=-2\) is a vertical line (undefined slope).

Step2: Analyze the line \(y = 10\)

The line \(y = 10\) is a horizontal line (slope \(m = 0\)).

Step3: Determine the relationship

A vertical line and a horizontal line are perpendicular.

Step4: Analyze the lines \(y = 5\) and \(y=-3\)

Both lines \(y = 5\) and \(y=-3\) are horizontal lines. Horizontal lines have the same slope (\(m = 0\)).

Step5: Determine the relationship

Lines with the same slope are parallel.

Step6: Analyze the line parallel to \(y = 7\)

The line \(y = 7\) is a horizontal line (\(m=0\)). A line parallel to it will also be horizontal (\(m = 0\)). The equation of a horizontal line is of the form \(y = k\). Since it passes through \((-1,-10)\), the \(y\)-coordinate of all points on the line is \(-10\). So the equation is \(y=-10\).

Step7: Analyze the angle in the rectangle

In a rectangle, adjacent angles are supplementary. Let \(\angle1\) and the \(116^{\circ}\) angle be related. Since the sum of adjacent angles formed by a trans - versal cutting two parallel lines (sides of the rectangle) is \(180^{\circ}\).

$$ \angle1+116^{\circ}=180^{\circ} $$

$$ \angle1=180^{\circ}-116^{\circ} $$

$$ \angle1 = 64^{\circ} $$

Answer:

1. perpendicular
2. parallel
3. \(y=-10\)
4. \(64\)