Consider the values in each table. State whether they could represent a directly proportional relationship between x and y:
| x | 1 | 3 | 5 | 7 |
|---|---|---|---|---|
| y | 50 | 40 | 30 | 20 |
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 5 | 20 | 45 | 80 |
| x | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| y | 5 | 10 | 15 | 20 |
| x | 1 | 5 | 6 | 20 |
|---|---|---|---|---|
| y | 100 | 75 | 50 | 25 |
The diagram shows the graph of a straight line with positive gradient.
As x decreases towards -\infty, describe what happens to y?
As x increases towards \infty, describe what happens to y?
A straight line graph has a positive y-intercept and a positive x-intercept. Determine whether the following statements are true of this line graph.
Is the straight line graph increasing or decreasing?
Can we determine whether the straight line graph is steeper than y = x? Explain your answer.
For the following equations:
y = - 2 x
y = - 1 - \dfrac{9 x}{2}
For the following equations:
y = 6 \left( 3 x - 2\right)
5 x - 30 y - 25 = 0
Find the gradient of the line that passes through the given points:
\left( - 3 , - 1 \right) and \left( - 5 , 1\right)
\left( - 3 , 4\right) and \left(1, 4\right)
\left(2, - 6 \right) and the origin
Find the gradient of the line going through points A and B.
We want to determine if the points A \left(3, - 2 \right), B \left(5, 4\right) , and C \left(1, - 8 \right) are collinear:
Find the gradient of the line through A and B.
Find the gradient of the line through A and C.
Hence, state the gradient of the line through B and C.
Are the points A, B and C collinear?
Points P(-1,-1), Q(0, 1), R(-1, 6) andS(-2, 4) are plotted on the number plane shown. What type of quadrilateral is PQRS? Justify your answer with mathematical working.
Find the value of the unknown given the following:
A line passing through the points \left( - 1 , 4\right) and \left( - 4 , t\right) has a gradient equal to - 3.
A line passes through the points \left(11, c\right) and \left( - 20 , 16\right) and has a gradient of - \dfrac{4}{7}.