Question

Which of the following lines is parallel to x = 7? (2 points) a 3y = 7 b y = 7 c x = y d x = 4

Answer 1

Answer:

Choice d. $l:x = 7$ is parallel to the line $x = 4$.

Step-by-step explanation:

Refer to the diagram attached. (Created with GeoGebra)

The line $x = 7$ is made of all the points on a cartesian plane that meet the requirement $x = 7$. In other words, this line consists of points with x-coordinate $7$. That includes:

• $(7, -1)$,
• $(7,0)$, and
• $(7,1)$.

That line is perpendicular to the x-axis (the horizontal axis) and intersects the x-axis at the point $(7,0)$.

Now, consider the lines in the choices.

The first line $3y =7$ requires only that the y-coordinates of its points be 7/3. This line accepts any x-values. Points on this line include:

• $\displaystyle \left(-1, \frac{7}{3}\right)$,
• $\displaystyle \left(0, \frac{7}{3}\right)$, and
• $\displaystyle \left(-1, \frac{7}{3}\right)$.

As a result, this line is parallel to the y-axis and is perpendicular to the line $x = 7$.

Similar to the first, the second line $y = 7$ is also parallel to the y-axis and is perpendicular to the line $x = 7$.

The third line $x = y$ requires that the x- and y- coordinates of all its points be equal. Points may include:

• $(-1, -1)$,
• $(0,0)$, and
• $(1,1)$.

This line is slant.

The last line $x = 4$ is similar to the given line $x = 7$. This line is also perpendicular to the x-axis. The difference is that this line is three units to the left of the line $x = 7$.