Lines — Quiz 3

Questions in this quiz (7)

1. In the given pair of equations, $$a$$ and $$b$$ are constants. The graph of this pair of equations in the $$xy$$-plane is a pair of perpendicular lines. Which of the following pairs of equations represents a pair of perpendicular lines?

   • $$4x+5y=3$$ and $$ax-by=7$$
   • $$4x+5y=3$$ and $$ax+by=7$$
   • $$4x+5y=3$$ and $$2ax+5by=7$$
   • $$8x-10y=6$$ and $$ax+by=7$$

2. Line $$p$$ has an equation of $$y=-2x+4$$. If line $$q$$ is parallel to line $$p$$, and line $$q$$ passes through the points $$(-1,3)$$ and $$(x,-1)$$, what is the value of $$x$$?

   • -3
   • 1
   • -2
   • -4

3. A line has an x-intercept of $$-3$$ and a y-intercept of $$6$$. What is the equation of this line?

   • $$y=-x+6$$
   • $$y=2x+3$$
   • $$y=x+6$$
   • $$y=2x+6$$

4. What is the slope of a line in the standard $$xy$$-coordinate plane containing the points $$(x, x^2)$$ and $$(y, y^2)$$?

   • $$x + y$$
   • $$x - y$$
   • $$y - x$$
   • $$\frac{y^2 - x^2}{y - x}$$

5. Line A passes through the points $$(2,3)$$ and $$(4,5)$$. Line B passes through the point $$(1,-2)$$. What must be the $$y$$-intercept of line B in order for line A and line B to intersect at a $$90^\circ$$ angle?

   • $$1$$
   • $$-2$$
   • $$-1$$
   • $$2$$

6. A line $$p$$ has the equation $$y = -x + 6$$. Line $$q$$ has a slope that is 4 times that of line $$p$$, and it passes through the point $$(1, 2)$$. If $$(3, k)$$ is another point on line $$q$$, what is the value of $$k$$?

   • -6
   • -4
   • 4
   • -1

7. The line $$y = mx + 4$$, where $$m$$ is a constant, is graphed in the $$xy$$-plane. If the line passes through the point $$(p, q)$$, which is not on the $$x$$- or $$y$$-axis, what is the slope of the line in terms of $$p$$ and $$q$$?

   • $$\frac{p - 4}{q}$$
   • $$\frac{p - 4}{p}$$
   • $$\frac{q - 4}{p}$$
   • $$\frac{q}{p-4}$$