For the following graphs:
State the value of the x-intercept.
State the value of the y-intercept.
For each of the following tables of values:
Find the slope, a.
Find the y-intercept, b.
Write the equation of the line expressing the relationship between x and y.
Complete the table of values.
| x | 0 | 1 | 2 | 3 | 4 | 24 |
|---|---|---|---|---|---|---|
| y | 0 | 4 | 8 | 12 | 16 |
| x | 0 | 1 | 2 | 3 | 4 | 21 |
|---|---|---|---|---|---|---|
| y | 9 | 14 | 19 | 24 | 29 |
| x | 0 | 1 | 2 | 3 | 4 | 25 |
|---|---|---|---|---|---|---|
| y | - 23 | - 21 | - 19 | - 17 | - 15 |
| x | 0 | 1 | 2 | 3 | 4 | 70 |
|---|---|---|---|---|---|---|
| y | 27 | 22 | 17 | 12 | 7 |
For each of the following tables of values:
Find the equation of the line expressing the relationship between x and y.
Complete the table of values.
| x | 1 | 2 | 3 | 4 | 19 |
|---|---|---|---|---|---|
| y | 5 | 10 | 15 | 20 |
| x | 1 | 2 | 3 | 4 | 16 |
|---|---|---|---|---|---|
| y | - 3 | - 6 | - 9 | - 6 |
| x | 1 | 2 | 3 | 4 | 60 |
|---|---|---|---|---|---|
| y | 1 | 4 | 7 | 10 |
| x | 1 | 2 | 3 | 4 | 80 |
|---|---|---|---|---|---|
| y | - 14 | - 22 | - 30 | - 38 |
| x | 1 | 2 | 3 | 4 | -15 |
|---|---|---|---|---|---|
| y | 82 | 74 | 66 | 58 |
Find the equation that corresponds to each of the following tables:
| x | - 1 | 0 | 1 | 2 | 3 |
|---|---|---|---|---|---|
| y | 7 | 4 | 1 | - 2 | - 5 |
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 5 | 8 | 11 | 14 | 17 |
| x | - 8 | - 7 | - 6 | - 5 | - 4 |
|---|---|---|---|---|---|
| y | - 37 | - 32 | - 27 | - 22 | - 17 |
| x | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|
| y | -1 | - 3 | - 5 | - 7 | - 9 |
Find the equation of the following lines:
A line that passes through the point A \left( - 5 , - 4 \right) and has a slope of - 4.
A line that passes through the point A \left( - \dfrac{4}{5} , - 4 \right) and has a slope of 2.
A line that passes through Point A \left( - 4 , 3\right) and has a slope of 4.
A line that passes through Point A \left(7, - 6 \right) and has a slope of - 3.
A line that passes through the point A \left(3, 5\right) and has a slope of - \dfrac{5}{2}.
A line that passes through the point A \left(4, 3\right) and has a slope of - 3\dfrac{1}{3}.
A line that passes through the point A \left( - 4 , 3\right) and has a slope of - 9.
A line that passes through the point A \left( - \dfrac{5}{9} , 7\right) and has a slope of 7.
A line that passes through the point A \left(8, 1\right), and has a slope of \dfrac{5}{2}.
A line that passes through the point A \left( - 4 , 5\right) and has a slope of 3\dfrac{1}{2}.
For each of the following lines:
Find the equation of the line.
Sketch the graph of the line.
A line has slope 2 and passes through the point \left( - 5 , - 3 \right).
A line has slope - \dfrac{3}{2} and passes through the point (- 2, 2).
A line has slope - \dfrac{2}{5} and passes through the point \left( - 10 , 2\right).
A line has slope - 3 and passes through the point \left(2, - 12 \right).
Consider the line with equation 2 x + y = 8 .
Find the x-intercept of the line.
Hence, find the equation of a line with a slope of - 4 that passes through the x-intercept of the given line.
Find, in general form, the equation of a line which has a slope of \dfrac{4}{7} and cuts the x-axis at - 10.
For each of the following lines:
Find the slope of the line.
Find the equation of the line.
A line passes through the points \left(2, - 7 \right) and \left( - 5 , 6\right).
A line passes through the points \left(3, - 3 \right) and \left(5, - 11 \right).
A line passes through the points A \left( - 6 , 7\right) and B \left( - 8 , - 4 \right).
Identify which of the following equations of straight lines have a slope of 5 and pass through the point A \left(-1, - 4 \right):
\dfrac{y + 4}{x + 1} = 5
\dfrac{x + 1}{y + 4} = 5
\dfrac{- 4 - y}{-1 - x} = 5
\dfrac{y + 1}{x + 4} = 5
Write down the equations of three lines that pass through the point (1, 3). Explain how your lines are different.
Find the equation of the following lines:
A line that is parallel to the x-axis and passes through \left( - 10 , 2\right).
A line that is parallel to the y-axis and passes through \left( - 7 , 2\right).
A line that is parallel to the line y = - 3 x - 8 and cuts the y-axis at - 4.
A line goes through A \left(3, 2\right) and B \left( - 2 , 4\right):
Find the slope of the given line.
Find the equation of another line that has a y-intercept of 1 and is parallel to this line.
Consider line L_1 with equation: 5 x - 4 y + 2 = 0.
Find the slope of a line, L_2, that is parallel to L_1.
Find the equation of L_2 using the point-slope formula, given that it passes through Point A \left( - 4 , 6\right). Express the equation in general form.
Find the equation of the following lines:
Passes through the point \left(9, - 5 \right) and is parallel to the line y = - 5 x + 2.
Passes through the point \left(-2, -4\right) and is parallel to the line y = 2x+13.
Passes through the point \left(10, 6\right) and is parallel to the line y = -6x-4.
Passes through the point \left(-3, 7\right) and is parallel to the line y = -12x+5.
A line has a slope of \dfrac{3}{10} and passes through the midpoint of A \left( - 6 , - 6 \right) and B \left(8, 8\right).
Find the coordinates of M, the midpoint of AB.
Find the equation of the line in general form.
Consider the lines L_{1}, y = - 4 x + 5, and L_{2}, y = x - 1.
Find the midpoint M of their y-intercepts.
Find the equation of the line that goes through the point M and has slope \dfrac{1}{3}. Express the equation in general form.
A circle with centre C \left(11, 13\right) has a diameter with end points A \left(5, 14\right) and B \left(p, q\right).
Find the value of p.
Find the value of q.
Find the equation of the line passing through B with slope \dfrac{9}{2}.
There are 24 litres of water in a rainwater tank initially. It then rains at a constant rate for 24 hours. The tank fills up at a rate of 4 liters per hour.
Complete the table of values.
| \text{Number of hours passed } (n) | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| \text{Volume of water in liters }(W) |
Graph the linear relationship on a number plane.
Write an equation relating the volume of water in litres (W) in terms of the hours passed (n).
The water tank only has a capacity of 64 litres. After how many hours will the tank begin to overflow?
After Sally starts running, her heartbeat increases at a constant rate as shown in the table below:
| \text{Number of minutes passed} \left( x \right) | 0 | 2 | 4 | 6 | 8 | 10 | 12 |
|---|---|---|---|---|---|---|---|
| \text{Heart rate} \left( y \right) | 69 | 73 | 77 |
Complete the table.
Find the unit change in y for the above table.
Determine the equation of the line in slope-intercept form that describes the relationship between the number of minutes passed, x, and Sally’s heartbeat, y.
What does the slope represent in context?
The following graph shows the relationship between the number of Canadian Geese in the Boreal Shield Ecozone (in thousands), \\C, and the time in years, t, since 1970.
Write the equation describing this relationship.
To ensure patients get a constant rate of a medication an IV pump is used. 80 \text{ mL} of medication needs to be administered to a patient. The graph shows the amount of medication remaining over time.
How long will it take for all of the medication to be given?