Lines — Quiz 5

Questions in this quiz (9)

1. A line passes through the origin and through the point $$Q = (2, 4)$$. If you were to draw a new line perpendicular to the first that also passes through $$Q$$, what would be the equation of this new line?

   • $$y=-\frac{4}{2}x+5$$
   • $$y=-\frac{1}{2}x - 2$$
   • $$y=-\frac{1}{2}x - 5$$
   • $$y=-\frac{1}{2}x + 5$$

2. Assume line $$p$$ has the equation $$y = 2x$$ and line $$q$$ is parallel to $$p$$. If line $$q$$ passes through the point $$(4, 3)$$, what is the equation for line $$q$$?

   • $$y = 2x + 3$$
   • $$y = 2x - 5$$
   • $$y = 2x - 4$$
   • $$y = 2x + 1$$

3. The table gives the coordinates of two points on a line in the $$xy$$-plane:The $$y$$-intercept of the line is $$(m - 3, c)$$, where $$m$$ and $$c$$ are constants. What is the value of $$c$$?

   • 18
   • 38
   • 6
   • -6

4. While doing a math assignment, Max was supposed to graph the line $$y=3x-5$$ in the standard $$(x,y)$$ coordinate plane. However, he mistakenly swapped the $$x$$ and $$y$$ coordinates of all his points. For example, he plotted $$(2,1)$$ instead of $$(1,2)$$. What is the equation of the line that Max mistakenly graphed?

   • $$y=-3x+5$$
   • $$y=\frac{-1}{3}x+\frac{3}{5}$$
   • $$y=3x+\frac{1}{3}$$
   • $$y=\frac{1}{3}x+\frac{5}{3}$$

5. Lines $$p$$ and $$q$$ are perpendicular. If the equation of line $$p$$ is $$y=mx+c$$ and the lines intersect at point $$(4,5)$$, which point lies on line $$q$$?

   • $$(4+2m,5)$$
   • $$\left(4-\frac{1}{m},5\right)$$
   • $$(4-3m,5+2m)$$
   • $$(4+m,5-2m)$$

6. Line $$p$$ has a positive slope and a negative y-intercept. Line $$q$$ is parallel to line $$p$$ and has a positive $$x$$-intercept. The $$y$$-intercept of line $$q$$ must be:

   • Positive
   • Zero
   • Negative
   • Not known

7. Determine whether the three points are collinear (on a single line): $$P(0,1),Q(3,4),R(6,7)$$

   • Collinear
   • Not collinear
   • Depends on the distance PR
   • Not known

8. Find the equation of line $$l$$ that is exactly halfway between the lines$$m : y = -2x + 7$$ and $$n : y = -2x - 3$$

   • $$y = -2x + 4$$
   • $$y = -2x - 4$$
   • $$y = -2x + 2$$
   • $$y = 2x + 5$$

9. Regardless of the value of parameter $$k$$, the line$$(k+2)x + (3k - 4)y + 5 = 0$$ passes through a fixed point. Find this point.

   • $$(-1.5, 0.5)$$
   • $$(-3, 1.5)$$
   • $$(-3, 1.5)$$
   • $$(-0.5, -3)$$