4.04 Linear graphs
Consider the equation y = 2 x - 4.
Complete the table of values:
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y |
Sketch the line that passes through these points.
For each of the following equations:
Complete a table of values of the form:
| x | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
Sketch the graph of the line on a number plane.
y = x + 9
y = 3 x + 3
y = 4 x
y = - x + 1
For each of the following equations:
Complete the table of values:
| x | - 3 | 0 | 3 | 6 |
|---|---|---|---|---|
| y |
Sketch the graph of the line on a number plane.
y = - 3 x -1
y = \dfrac{x}{3} + 2
Consider the equation y = - \dfrac{3 x}{2} + 6.
Complete the table of values:
| x | - 2 | 0 | 2 | 4 |
|---|---|---|---|---|
| y |
Sketch the graph of the line on a number plane.
Consider the equation y = - x - 2.
Complete the table of values:
| x | - 1 | 0 | 1 |
|---|---|---|---|
| y |
Sketch the line on a number plane.
Find the coordinates of the y-intercept.
Find the coordinates of the x-intercept.
Find the y-value when x = 3.
Find the x-value when y = -4.
Consider the equation 2 x - 3 y - 18 = 0.
Complete the table of values:
| x | - 3 | 0 | 3 |
|---|---|---|---|
| y |
Sketch the line on a number plane.
Find the coordinates of the y-intercept.
Find the coordinates of the x-intercept.
Find the y-value when x = 6.
Sketch the following lines on a number plane:
A line that passes through the point \left( - 1 , 2\right) and has a gradient of 4.
A line that passes through the point \left( - 1 , 8\right) and has a gradient of - 2.
A line that passes through the point \left(3, 5\right)and has a gradient of 5.
A line that passes through the point \left( - 2 , 4\right) and has a gradient of- 3.
For each of the following equations of lines:
Find the gradient of the line.
Find the coordinates of the point on the line where x=0.
Sketch the line on a number plane.
y = 3 x - 3
y = - 2 x -1
y = x - 1
For each of the following equations of lines:
Find the x-intercept of the line.
Find the y-intercept of the line.
Sketch the line on a number plane.
For the following linear equations:
Find the coordinates of the y-intercept.
Find the coordinates of the x-intercept.
Sketch the line.
y = 2 x - 2
y = - 2 x + 4
y = - \dfrac{4 x}{3}
y = - 3 x + 6
For each of the following equations:
Find the y-value of the y-intercept of the line.
Find the x-value of the x-intercept of the line.
Find the value of y when x = -1.
Sketch the equation of the line on a number plane.
Sketch the following lines using the y-intercept and any other point on the line:
y = x + 5
y = 3 x - 4
y = - x - 5
y = - 4x + 7
Find the x-intercept of the line - x - 8 y = 8.
For each of the following equations:
Solve for the x-intercept of the line.
Solve for the y-intercept of the line.
Sketch the line on a number plane.
3 x + y - 1 = 0
- 6 x + 2 y + 18 = 0
Sketch the following lines using the gradient and y-intercept:
Sketch the following lines on a number plane:
A line that has a y-intercept of - 2 and whose gradient is 4.
A line that has a y-intercept of 8 and whose gradient is - 4.
A line that has a y-intercept of 2 and whose gradient is \dfrac{1}{2}.
A line that has a y-intercept of 7 and whose gradient is - \dfrac{3}{4}.
A line that has an x-intercept of 3 and whose gradient is 2.
A line that has an x-intercept of - 2 and whose gradient is 3.
A line that has an x-intercept of - 5 and whose gradient is - 3.
A line that has an x-intercept of - 8 and whose gradient is - 1.
Sketch the following lines on the number plane:
y = 3
x = 7
y = - 5
x = - 6
y = 8
x = 7
y = - 2
y = 0
Sketch the following lines:
The line parallel to the x-axis and passes through the point \left(3, - 5 \right).
The line parallel to the y-axis and passes through the point \left( - 8 , 3\right).
The line perpendicular to the x-axis and passes through the point \left(3, - 8 \right).
The line perpendicular to the y-axis and passes through the point \left(3, - 4 \right).