Question 1
LEVEL 4
Find which, if any, of the following lines are parallel.
a) 3y-9x=18
b) \dfrac{1}{3}y=x-7
c) 2y+x=1
d) 2y=6x-18
e) 4y=8x-4
Select the correct answer from the list below:
A: c and d
B: c, d, and e
C: a, b, and c
D: a,b, and d
CORRECT ANSWER: D: a,b, and d
WORKED SOLUTION:
To find out which lines are parallel we need to change them into the form y=mx+c and compare the m values.
Line a
3y-9x=18
Add 9x to both sides
3y=9x+18
Divide both sides by 3
y=3x+6
m=3
Line b
\dfrac{1}{3}y=x-7
Multiply both sides by 3
y=3x-21
m=3
Line c
2y+x=1
Subtract x from both sides
2y=-x+1
Divide both sides by 2
y=-\frac{1}{2}x+\frac{1}{2}
m=-\frac{1}{2}
Line d
2y=6x-18
Divide both sides by 2
y=3x-9
m=3
Line e
4y=8x-4
Divide both sides by 4
y=2x-1
m=2
Comparing m values we can see that lines a, b, and d are the same, so are parallel.
Question 2
LEVEL 4
Plot the graph, from x=-3 to x=1, of the straight line that is parallel to the line 3y=6x-3 and passes through the point (-1,0).
Select the correct graph from the list below:
A:
B:
C:
D:
CORRECT ANSWER: B
WORKED SOLUTION:
We need to change this equation into the form y=mx+c to find its gradient, which we do by dividing both sides by 3.
3y=6x-3
y=2x-1
To draw our parallel line from the point, we need to find this point, read across 1 and then up 2. Doing this will give us two points on our line.
And now, all we need to do is connect these points with a straight line.
Question 3
LEVEL 4
Choose the equation that is parallel to the line in the following graph.
Select the correct answer from the list below:
A: y = \frac{1}{2}x + 4
B: y = - \frac{1}{2}x + 3
C: y = 2x
D: y = -2x + 11
CORRECT ANSWER: A: y = \frac{1}{2}x + 4
WRITTEN SOLUTION:
The line in the graph has equation y = \frac{1}{2}x + 1
Therefore any line parallel to this must have the same gradient, \frac{1}{2}
The only equation with the same gradient is y = \frac{1}{2}x + 4, by looking at the coefficient before the x
Question 4
LEVEL 4
Choose the equation that is parallel to the line in the following graph and passes through the point (-2,-4)
Select the correct answer from the list below:
A: y = \frac{3}{2}x - 1
B: y = \frac{2}{3}x - 1
C: y = \frac{3}{2}x
D: y = - \frac{2}{3}x +2
CORRECT ANSWER: A: y = \frac{3}{2}x - 1
WRITTEN SOLUTION:
The line in the graph has equation y = \frac{3}{2}x + 1
Therefore any line parallel to this must have the same gradient, \frac{3}{2}
The only equations with the same gradient are y = \frac{3}{2}x - 1 and y = \frac{3}{2}x, by looking at the coefficient before the x
We can look at the graph or substitute values of x=-2 and y=-4 into the equation y = \frac{3}{2}x + c to find the value of c
In doing so, we find that the y-intercept, c, is -1
Therefore the correct equation is y = \frac{3}{2}x - 1
Question 5
LEVEL 4
Choose the equation that is parallel to the line with equation y +3x = 5.
Select the correct answer from the list below:
A: y = -3x
B: y = 3x + 3
C: y = - \frac{1}{3}x + 1
D: y = \frac{1}{3}x +5
CORRECT ANSWER: A: y = -3x
WRITTEN SOLUTION:
We first need to rearrange the equation of the line to get it in the form y=mx+c
Subtracting 3x from both sides gives y = -3x+5
Any line parallel to this must have the same gradient, -3
The only equation with the same gradient is y = -3x, by looking at the coefficient before the x