Determine the slope of the line that passes through each of the following pairs of points:
Point A\left( - 1 , 0\right) and Point B\left(0, 3\right)
Poit A\left(2, - 6 \right) and the origin
Point A\left(4, 1\right) and Point B\left(11, - 6 \right)
Point A\left( - 3 , - 1 \right) and Point B\left( - 5 , 1\right)
Point A\left(0, - 4 \right) and Point B\left(5, -1\right)
Point A\left( - 7 , - 6 \right) and Point B\left( - 5 , - 8 \right)
Point A\left( - 3 , 4\right) and Point B\left(1, 4\right)
Point A\left(3, 4\right) and Point B\left(5, 4\right)
Determine whether the each of the following pairs of coordinates will have a slope that is defined or undefined.
\left( - 10 , 5\right) and \left( - 10 , 12\right)
\left(10, 5\right) and \left(10, 1\right)
\left(10, - 1 \right) and \left( - 10 , - 1 \right)
\left( - 10 , 5\right) and \left(10, 5\right)
\left(10, 7\right) and \left(10, 2\right)
\left(10, - 2 \right) and \left( - 10 , - 2 \right)
\left( - 10 , 7\right) and \left( - 10 , 12\right)
\left( - 10 , 7\right) and \left(10, 7\right)
Consider the line y = 5 x + 5 that has been graphed on the number plane.
Find the y value of the point on the line where x = 4.
Using a = \dfrac{\text{rise }}{\text{run }}, the point found in the previous part and the y-intercept, find the slope of the line.
Given the slope of the line passing through the two points, find the value of the variable:
\left(4, - 3 \right) and \left(1, t\right), slope = - 2
\left(5, 3\right) and \left(2, t\right), slope = - 4
\left(5, 3\right) and \left(d, 63\right), slope = 4
\left(11, c\right) and \left( - 20 , 16\right), slope = - \dfrac{4}{7}
\left(1, 2\right) and \left( - 4 , t\right), slope=5
A paratrooper falls to the ground along a diagonal line. His fall begins 1157 \text{ m} above the ground, and the line he follows has a slope of 1.3. That is, he falls 1.3\text{ m} vertically for every 1\text{ m} he moves across horizontally. How far horizontally across the ground does he land from his initial position in the sky?
Consider the following graph:
Determine the slope of the line.
Find the y-value of the y-intercept of the line.
Does this line have an x-intercept?
Consider the following graph:
Determine the slope of the line.
Does this line have a y-intercept?
Identify the x-intercept of the line.
Consider the following graphs.
Determine whether the the slope is 0, undefined or neither.
Explain what it means if the slope of a line is:
undefined
zero
State whether each of the following statements is correct for vertical lines.
A vertical line's slope is very large because it is so steep.
A vertical line has a slope that is undefined because, when calculating the slope using the formula \dfrac{\text{rise }}{\text{run }}, the run is 0 and it is not possible to divide a number by 0.
A vertical line's slope is equal to 0 because when calculating the slope using the formula \dfrac{\text{rise }}{\text{run }}, the run is 0.
The line in the graph is nearly horizontal.
Which of the following is most likely to be its slope?
Consider the points on the graph.
Determine the slope of \overline{AB}.
Determine the slope of \overline{BC}.
The line that has been graphed is nearly vertical.
Which of the following is most likely to be its slope?
5
55
undefined
0.55
For each of the following intervals between points A and B:
Find the rise.
Find the run.
Find the slope.
A \left( - 8 , 4\right) and B \left( - 1 , 18\right)
A \left( - 5 , - 2 \right) and B \left(-1, 10\right)
A \left( - 2 , - 1 \right) and B \left(2, - 13 \right)
A \left( - 1 , 2\right) and B \left(1, - 4 \right)
Explain why a vertical line has an undefined slope.
State the slope of any line parallel to the x-axis.
Determine the slope of the following lines passing through points A and B:
Consider the line plotted, where A \left(2, 0\right) and B \left(0, 4\right) both lie on the line.
Determine the slope of the line.
As x increases, what happens to the value of y?
Determine the slope of the line that passes through the given points:
\left( - 1 , 0\right) and \left(0, 3\right)
\left( - 4 , 7\right) and \left(1, 10\right)
\left(1, - 4 \right) and the origin
\left(2, - 6 \right) and the origin
\left(6, 4\right) and \left(3, 4\right)
\left( - 6 , 5\right) and \left(4, 5\right)
\left( - 2 , - 5 \right) and \left( - 9 , - 12 \right)
\left( - 3 , - 1 \right) and \left( - 5 , 1\right)
Consider the points A \left( - 11 , - 9 \right), B \left( - 5 , 1\right) and C \left( - 2 , 6\right):
Determine the slope of AB.
Determine the slope of BC.
Do the points A, B and C lie in a straight line?
Consider the following points: A \left(26, m - 24\right), B \left( - 1 , m\right) and C \left( - 10 , 9\right).
Find m, given that A, B and C are collinear.
A \left( - 4 , - 2 \right), B \left(2, 1\right) and C \left(2, - 4 \right) are the vertices of a triangle.
Name the side of the triangle that is a vertical line.
Find the area of the triangle.
The 4 vertices of square ABCD have been plotted on a number plane.
Find the slope of side AB.
Find the slope of side BC.
Find the product of the slopes in parts (a) and (b).
If two lines are perpendicular their slopes multiply to -1. Are sides AB and BC perpendicular?
A certain ski resort has two ski runs.
Find the slope of ski slope A. Give your answer as a decimal to two decimal places.
Find the slope of ski run B. Give your answer as a decimal to two decimal places.
Which run is steeper, A or B?
A diver starts at the surface of the water and starts to descend below the surface at a constant rate. The table shows the depth of the diver over 5 minutes.
| Number of minutes passed | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Depth of diver in meters | 0 | 0.8 | 1.6 | 2.4 | 3.2 |
Graph the linear relationship represented in the table.
What is the increase in depth each minute?
State the slope of the line.
Calculate the depth of the diver after 24 minutes.
While filling a pool 72 centimeters deep, Victoria notices it has taken 3 hours to fill it up to a depth of 36 centimeters.
At what rate, in meters per hour, is the pool being filled up?
At this rate, Victoria estimates that it will take her 6 hours to fill up the pool. Is she correct?
David wants to buy a new cellphone plan. The table and graph below represent two different offers from Mobile Mogul and Phone Frenzy.
Mobile Mogul
Phone Frenzy
| Minutes of talk time | 10 | 20 | 30 | 40 |
|---|---|---|---|---|
| Cost (dollars) | 33.00 | 66.00 | 99.00 | 132.00 |
Calculate the rate of change for Mobile Mogul.
Calculate the rate of change for Phone Frenzy.
Which of the options offers the cheaper rate of calling?
A water tank is being pumped out. The graph below show the amount of water left in liters compared to the time spent pumping, in minutes.
Find the rate of change of the volume of water in the tank.
The amount of time it takes Xanthe to make beaded bracelets is shown on the graph.
Complete the following statement:
Xanthe can make ⬚ bracelets every ⬚ hours.
The number of batches of cookies that can be made in a bakery every houris shown in the following graph.
Find the slope of the line.
What does the slope represent in terms of the situation?
The price for playing arcade games is shown in the following graph.
Find the slope of the line.
What does the slope represent in terms of the situation?
While playing a particular song, a pianist is measured to make an average of 40 keystrokes every 8 seconds.
Complete the table of values:
| Time (in seconds) | 0 | 4 | 8 | 16 | 24 |
|---|---|---|---|---|---|
| Keystrokes |
Construct a graph of the relationship between the number of seconds passed and the number of keystrokes made.
How many keystrokes is the pianist making per second?
In the following table, y represents the total rent paid on a house, in dollars, that has been rented for x weeks.
Find the weekly cost of rent.
| x | y |
|---|---|
| 10 | 3150 |
| 20 | 6300 |
| 30 | 9450 |
| 40 | 12,600 |
| 50 | 15,750 |