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:Choice d. [tex]l:x = 7[/tex] is parallel to the line [tex]x = 4[/tex].Step-by-step explanation:Refer to the diagram attached. (Created with GeoGebra)The line [tex]x = 7[/tex] is made of all the points on a cartesian plane that meet the requirement [tex]x = 7[/tex]. In other words, this line consists of points with x-coordinate [tex]7[/tex]. That includes:[tex](7, -1)[/tex],[tex](7,0)[/tex], and[tex](7,1)[/tex].That line is perpendicular to the x-axis (the horizontal axis) and intersects the x-axis at the point [tex](7,0)[/tex].Now, consider the lines in the choices.The first line [tex]3y =7[/tex] requires only that the y-coordinates of its points be 7/3. This line accepts any x-values. Points on this line include:[tex]\displaystyle \left(-1, \frac{7}{3}\right)[/tex],[tex]\displaystyle \left(0, \frac{7}{3}\right)[/tex], and[tex]\displaystyle \left(-1, \frac{7}{3}\right)[/tex].As a result, this line is parallel to the y-axis and is perpendicular to the line [tex]x = 7[/tex].Similar to the first, the second line [tex]y = 7[/tex] is also parallel to the y-axis and is perpendicular to the line [tex]x = 7[/tex].The third line [tex]x = y[/tex] requires that the x- and y- coordinates of all its points be equal. Points may include:[tex](-1, -1)[/tex],[tex](0,0)[/tex], and[tex](1,1)[/tex].This line is slant.The last line [tex]x = 4[/tex] is similar to the given line [tex]x = 7[/tex]. This line is also perpendicular to the x-axis. The difference is that this line is three units to the left of the line [tex]x = 7[/tex].