For each of the following linear equations:
Find the coordinates of the y-intercept.
Find the gradient.
Sketch the graph using the gradient and y-intercept.
y = x + 1
y = 4 x-1
y = 3 x - 1
y = - x + 4
y = -6x+2
y = - 3 x - 4
y = \dfrac{x}{3} + 3
y = \dfrac{1}{2} x - 2
Sketch the graph of each linear equation using the gradient and y-intercept:
2y = 3x-8
6x-3y=9
2x+5y=0
For each of the following, sketch the graph of the line:
Which passes through the point \left(0, -10\right) and has a gradient of 5.
Which passes through the point \left( - 2 , 4\right) and has a gradient of - 3 .
Sketch the graph of the following lines given the y-intercept and gradient:
A y-intercept of -2 and gradient of 5.
A y-intercept of 2 and gradient of - \dfrac{5}{4}.
A y-intercept of 7 and gradient of - 1.
A y-intercept of - 3 and gradient of - \dfrac{2}{5}.
For the following equations:
Find the y-intercept.
Find the x-intercept.
Sketch the graph of the line.
3 x + y + 2 = 0
Consider the equation y = - 2 x.
Find the value of the y-intercept.
Find the value of the x-intercept.
Find the value of y when x = 2.
Sketch the graph of the line.
Consider the equation 2 x - y - 2 = 0.
Complete the table of values:
Sketch the graph of the line.
State the coordinates of the axes intercepts.
Find x when y = - 5.
| x | - 1 | 0 | 1 | 4 |
|---|---|---|---|---|
| y |
For each of the following linear equations:
Complete the table of values.
Sketch the graph of the line.
y = 2 x - 4
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y |
y = - 2 x + 4
| x | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| y |
y = \dfrac{5 x}{3} - 5
| x | 0 | 3 | 6 | 9 |
|---|---|---|---|---|
| y |
Consider the given table for the linear equation x = 0 :
Does this represent the y-axis or x-axis?
| x | 0 | 0 | 0 | 0 |
|---|---|---|---|---|
| y | - 5.5 | - 2.5 | 3.5 | 6.5 |
State whether the following statements are true or false for vertical lines:
A vertical line's gradient is very large because it is so steep.
A vertical line has a gradient that is undefined, because when calculating the gradient 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 gradient is equal to 0, because when calculating the gradient using the formula \dfrac{\text{rise }}{\text{run }}, the run is 0.
State whether the following statements are true or false when the gradient of a line is zero:
The line is horizontal.
The line is vertical.
The change in y is equal to zero.
The change in x is equal to zero.
The change in y is equal to the change in x.
Consider the graphed line below:
State the gradient of the line.
Does this line have a y-intercept?
State the x-intercept of the line.
Hence write the equation of the line.
Consider the graphed line below:
Complete the table of values for the line:
| x | -3 | 0 | 1 | 4 |
|---|---|---|---|---|
| y |
Hence state the equation of the line.
For the following graphs:
State the coordinates of the y-intercept.
State the gradient of the line.
Write the equation of the line.
Consider the graphed line below:
Complete the table of values for the line:
| x | ||||
|---|---|---|---|---|
| y | 3 | 1 | 0 | -2 |
Hence state the equation of the line.
Sketch the graph of the following linear equations:
y = 4
x = 1
x = 0
y = 0
y = \dfrac{3}{2}
x = 4.5
y = - 3
x = - 6
x = - 8
State the equation of:
The x-axis.
The y-axis.
State the coordinates of the point of intersection of the following:
The line y = 5 and the line x = -2.
The horizontal line with y-intercept of 9 and the vertical line with x-intercept of -7.