ANSWER
QUESTION 17a
We were given the relation, [tex]y=15x[/tex], where y represents the number of new vocabularies learned, and x represents the number of weeks
Draw a horizontal line for number of weeks and a vertical line for number of vocabulary words using a scale of 5 units on both axes.
To graph this equation we need at least three points,
When
[tex]x=0[/tex], [tex]y=15(0)[/tex], [tex]\Rightarrow y=0[/tex]
So we plot the point [tex](0,0)[/tex]
When
[tex]x=1[/tex], [tex]y=15(1)[/tex], [tex]\Rightarrow y=15[/tex]
So we plot the point [tex](1,15)[/tex]
When
[tex]x=2[/tex], [tex]y=15(2)[/tex], [tex]\Rightarrow y=30[/tex]
So we plot the point [tex](2,30)[/tex]
Using a straight edge we draw a straight line through these three points.
The equation of the line is of the form [tex]y=mx[/tex], where [tex]m=15[/tex] is the slope.
This tells us that the 15 new vocabulary words are learned each week.
QUESTION 17 B
To find the number of new vocabulary words learnt after 5 weeks, we plug in [tex]x=5[/tex] in to the equation.
[tex]y=15(5)[/tex]
This gives us
[tex]y=75[/tex]
Therefore after 5 weeks, you learn 75 new vocabulary words.
QUESTION 17 C
We find the number of vocabulary words learned after 4 weeks and subtract it from the number of vocabulary words learned after 6 weeks'
To find the number of new vocabulary words learnt after 4 weeks, we plug in [tex]x=4[/tex] in to the equation.
[tex]y=15(4)[/tex]
This gives us
[tex]y=60[/tex]
Therefore after 4 weeks, you learn 60 new vocabulary words.
To find the number of new vocabulary words learnt after 6 weeks, we plug in [tex]x=6[/tex] in to the equation.
[tex]y=15(6)[/tex]
This gives us
[tex]y=90[/tex]
Therefore after 6 weeks, you learn 90 new vocabulary words.
We now subtract to get
[tex]90-60=30[/tex]
Therefore you learn 30 more vocabulary words after 6 wees than after 4 weeks.
