Question

question 1 of 5 select the correct answer. which equation represents a line that is parallel to the y-axis, is perpendicular to the x-axis, and has an undefined slope? y = \frac{2}{7}x + \frac{7}{2} y = \frac{7}{2}x y = \frac{2}{7} x = \frac{7}{2}

Explanation:

Step1: Recall line properties

A line parallel to the \( y \)-axis (perpendicular to \( x \)-axis) has an undefined slope. Its equation is of the form \( x = c \) (constant), where \( c \) is a real number.

Step2: Analyze options

• Option 1: \( y=\frac{2}{7}x+\frac{7}{2} \) is a linear equation with slope \( \frac{2}{7} \) (defined), not parallel to \( y \)-axis.
• Option 2: \( y=\frac{7}{2}x \) has slope \( \frac{7}{2} \) (defined), not parallel to \( y \)-axis.
• Option 3: \( y=\frac{2}{7} \) is horizontal (parallel to \( x \)-axis), slope \( 0 \) (defined).
• Option 4: \( x=\frac{7}{2} \) is vertical (parallel to \( y \)-axis, perpendicular to \( x \)-axis), slope undefined.

Answer:

\( x = \frac{7}{2} \) (the option with \( x = \frac{7}{2} \))