For each of the following linear equations:
State the gradient of the line.
State the y-intercept of the line.
Consider the following graph:
State the gradient of the line.
Does this line have a y-intercept?
State the x-intercept of the line.
Which of the following linear relationships represents a more rapid change in the value of y?
| x | 0 | 1 | 2 |
|---|---|---|---|
| y | 3 | 6 | 9 |
Which of the following linear relationships has a larger x-intercept?
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 |
For each of the given graphs, state the gradient of the line going through points A and B:
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 slope 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 straight line shown in the following graph:
Does the line y = 6 x + 1 have a larger or smaller rate of change than the graphed line?
Consider the straight line shown in the following graph:
Are the y-values of the line y = 6 x + 2 changing more or less rapidly than in the graphed line?
Consider the straight line shown in the following graph:
Does the line y = - 4 x + 6 have a larger or smaller y-intercept than the graphed line?
Find the equation of the following lines in gradient-intercept form:
A line that has a gradient of \dfrac{4}{3} and passes through the point \left(0, - 3 \right)
A line that has a gradient of \dfrac{2}{3} and passes through the point \left(0,3 \right)
A line that passes through the points A \left( - 6 , - 5 \right) and B \left(1, 6\right)
Find the equation of a line that has the same gradient as the line y = 7 - 3 x and the same
y-intercept as the line y = - 7 x - 8.
A line has gradient 5 and passes through the point \left( - 1 , - \dfrac{10}{3} \right). Find the equation of the line in general form.
A line has a gradient of - 2 and passes through the point \left( - 6 , - 3 \right). Find the equation of the line in gradient-intercept form.
A straight line passes through the point \left(0, \dfrac{3}{4} \right) with gradient 2.
Find the equation of the line in gradient-intercept form.
Find the equation of the line in general form.
Find the x-intercept of the line.
Consider the graph of the line:
What is the value of the y-intercept?
What is the gradient of the line?
Find the equation of the line in gradient-intercept form.
Rewrite the equation of the line in general form.
For the following graphed lines:
State the gradient.
State the y-intercept.
Write the equation of the line in gradient-intercept form.
Consider the line with equation 2 x + y - 8 = 0.
Find the x-intercept of the line.
Find the equation of a line with a gradient of - 4 that passes through the x-intercept of the given line.
For each of the following pairs of points:
Find the gradient of the line that passes through both points.
Find the equation of the line in gradient-intercept form.
\left(0, 6\right) and \left(3, 18\right)
\left( - 2 , - 9 \right) and \left( - 5 , 12\right)
\left( - 2 , 2\right) and \left( - 5 , 7\right)
\left(0, - 3 \right) and \left(1, 4\right)
Consider the equation of the line 5 x - 4 y + 20 = 0.
Find the x-intercept of the line.
Hence, find the equation of the line that passes through \left(2, 8\right) and the x-intercept. Write your answer in gradient-intercept form.
Consider the table of values below:
Is y increasing or decreasing?
For every 1 unit increase in x, by how much does y change?
Hence, find the algebraic rule linking x and y.
| x | 9 | 18 | 27 | 36 |
|---|---|---|---|---|
| y | -68 | -131 | -194 | -257 |
Write an equation for y in terms of x for the values in the given table:
| x | 0 | ... | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|
| y | -6 | ... | 18 | 21 | 24 | 27 |
A line has gradient - 2 and passes through the point \left( - 6 , - \dfrac{4}{3} \right). Find the equation of the line in general form.
For each of the following equations:
Rewrite the equation in gradient-intercept form.
Find the gradient of the line.
Find the y-intercept of the line.
y = 3 \left( - 4 x - 2\right)
y = 6 \left( 3 x - 2\right)
A line has the equation 3 x - y - 4 = 0.
Write the equation of the line in gradient-intercept form.
Find the gradient of the line.
Find the y-intercept of the line.
Find the equation of the vertical line that passes through the point \left(2, 3\right).
The rectangle PQRS has vertices at P\left(-4,-3\right), Q\left(-6,-3\right), R\left(-6,-5\right) and S\left(-4,-5\right).
Find the equation of the line PQ.
Is the line QR vertical or horizontal?
Find the equation of the line RS.
Is the line PS vertical or horizontal?
Find the equation of the line PS.
Sketch the graph of the following linear equations by finding any two points on the line:
y = - 3 x - 4
y = \dfrac{x}{3} + 3
- 6 x + 3 y + 24 = 0
Sketch the graph of the following linear equations using the gradient and y-intercept:
y = 4 x-1
y = \dfrac{1}{2} x - 2
Sketch the graph of the following linear equations by finding the x-intercept and the y-intercept:
6 x + 2 y - 12 = 0
- 20 x + 5 y - 40 = 0
Sketch the graph of the following linear equations:
y = - 3
x = - 6
Consider the equation y = - 4 x + 4.
Find the coordinates of:
The y-intercept
The x-intercept
Sketch the graph for this equation.
For each of the following linear equations:
Complete the table of values below.
Sketch the graph of the line.
| x | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
| x | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
| x | - 6 | - 4 | - 2 | 0 |
|---|---|---|---|---|
| y |
| x | - 5 | - 3 | 0 | 6 |
|---|---|---|---|---|
| y |
| x | - 3 | - 2 | - 1 | 0 |
|---|---|---|---|---|
| y |
| x | - 3 | - 2 | 0 | 1 |
|---|---|---|---|---|
| y |
Consider the equation y = - x - 2.
Complete the table of values:
Sketch the graph of the line.
State the coordinates of the axes intercepts.
Find x when y = - 4.
| x | - 1 | 0 | 1 | 3 |
|---|---|---|---|---|
| y |
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 |
Consider the equation y = - x.
Complete the table of values:
Sketch a graph for the line.
Does the point \left( 2.5 , - 2.5 \right) lie on the line?
| x | - 1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
Consider the equation y = - x + 1.
Complete the table of values:
Sketch a graph for the line.
Does the point \left( 1.5 , - 0.5 \right) lie on the line?
| x | -1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |