For the following line segments AB:
State the rise from A to B.
State the run from A to B.
Hence find the gradient of line segment AB.
Consider the straight line that passes through the points A, B, C and D.
Find the gradient of the line using the points A and D.
Find the gradient of the line using the points B and C.
Does it matter which two points on a line are used to find the gradient?
Find the gradient of the following lines:
Consider the following line, where A\left(4, 0\right) and B\left(1, 12\right) are both points on the line:
Find the gradient of the line.
As x increases, is the value of y increasing or decreasing?
Find the gradient of the lines that pass through:
Point A \left( - 1 , 0\right) and Point B \left(0, 3\right)
Point A \left(2, - 6 \right) and the origin
Point A \left(3, 5\right) and Point B \left(1, 8\right)
Point A \left(-2, 4\right) and Point B \left(-5, -1\right)
For the following graphs:
State the coordinates of the y-intercept.
Find the gradient of the line.
Consider the equation y = x and the table of values given below:
State the coordinates of the y-intercept.
As x increases, is the value of y increasing or decreasing?
Find the gradient of the line.
| x | - 3 | - 2 | -1 | 0 |
|---|---|---|---|---|
| y | - 3 | - 2 | -1 | 0 |
Consider the equation y = - x and the table of values given below:
State the coordinates of the y-intercept.
As x increases, is the value of y increasing or decreasing?
Find the gradient of the line.
| x | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y | 1 | 0 | -1 | - 2 |
Consider the equation y = 5 x and the table of values given below:
Find the coordinates of the y-intercept.
Find the gradient of the line.
| x | - 3 | - 2 | -1 | 0 |
|---|---|---|---|---|
| y | - 15 | - 10 | - 5 | 0 |
Consider the equation y = 2 x + 5:
Complete the given table of values:
State the coordinates of the y-intercept.
Find the gradient of the line.
| x | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
Consider the table of values:
State the coordinates of the y-intercept.
Find the gradient of the line.
| x | - 2 | 0 | 2 | 4 |
|---|---|---|---|---|
| y | 1 | 2 | 3 | 4 |
Consider the table of values:
State the coordinates of the y-intercept.
Find the gradient of the line.
| x | - 3 | 0 | 3 | 6 |
|---|---|---|---|---|
| y | -1 | -2 | -3 | -4 |
Sketch the graph of the following linear equations using the gradient and y-intercept:
y = x + 1
y = 4 x-1
y = 3 x - 1
y = - x + 4
y = -6x+2
y = \dfrac{1}{2} x - 2
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{1}{2}.
A y-intercept of 7 and gradient of - \dfrac{3}{4}.
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}.
Sketch the graph of the linear function that has a gradient of - 1 and an x-intercept of 4.
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.