Question

lines rs, tv, and sw are shown.
which statements are true about these lines? select three options.
line rs has a slope of 6.
line sw has an undefined slope.
line tv has a slope of 0.
lines rs and tv are parallel.
line sw is perpendicular to line rs, but not to line tv.

Explanation:

Step1: Find the slope of vertical lines

Vertical lines have an undefined slope. Lines \(RS\) and \(TV\) are vertical (since they are parallel to the \(y -\)axis). For a vertical line \(x = a\) (where \(a\) is a constant), the formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\), and \(x_2-x_1 = 0\). So, lines \(RS\) and \(TV\) have undefined slopes. Since two lines with the same (undefined) slope are parallel, lines \(RS\) and \(TV\) are parallel.

Step2: Find the slope of horizontal line \(SW\)

Line \(SW\) is horizontal (parallel to the \(x -\)axis). For a horizontal line \(y = b\) (where \(b\) is a constant), using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), \(y_2 - y_1=0\). So, the slope of line \(SW\) is \(m = 0\). A line with slope \(0\) (horizontal line) and a line with an undefined slope (vertical line) are perpendicular.

Answer:

Lines \(RS\) and \(TV\) are parallel; Line \(SW\) has a slope of \(0\); Line \(SW\) is perpendicular to line \(RS\) (and also to line \(TV\))