13.13 Finding the equation from a graph
Determine whether the following graphs are linear:
Consider the following graph:
Complete the table of values for the points shown on the line.
| x | -1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
State the values of the gradient m, and the y-intercept, c.
Given that the linear relationship is in the form y = m x + c, write the equation of the graph.
Hence find the coordinates for the point on the line when x = 21.
Consider the following graph:
Complete the table of values for the points shown on the line.
| x | -1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
State the values of the gradient m, and the y-intercept, c.
Hence write the linear equation for the graph.
Find the coordinates for the point on the line where x = 27.
Consider the following graph:
Complete the table of values for the points shown on the line:
| x | -2 | -1 | 0 | 1 |
|---|---|---|---|---|
| y |
State the values of the gradient m, and the y-intercept, c.
Hence write the equation for the graph.
Find the value of y when x = 40.
Consider the following graph:
Complete the table of values for the points shown on the line:
| x | -1 | 0 | 1 | 2 |
|---|---|---|---|---|
| y |
State the values of the gradient m, and the y-intercept, c.
Hence write the equation for the graph.
Find the value of y when x = 19.
Consider the following graph:
Complete the table of values for the points shown on the line:
| x | -5 | 0 | 5 | 10 |
|---|---|---|---|---|
| y |
When x increases by 5, by how much does y increase?
Hence when x increases by 1, by how much does y increase?
State the values of the gradient m, and the y-intercept, c.
Hence write the equation for the graph.
Find the coordinates for the point on the line where x = 35.
Consider the following graph:
Complete the table of values for the points shown on the line:
| x | -5 | 0 | 5 | 10 |
|---|---|---|---|---|
| y |
State the values of the gradient m, and the y-intercept, c.
Hence write the equation for the graph.
Find the coordinates for the point on the line where x = - 45.
Consider the following graph:
Complete the table of values for the points shown on the line:
| x | -5 | 0 | 5 | 10 |
|---|---|---|---|---|
| y |
State the values of the gradient m, and the y-intercept, c.
Hence write the equation for the graph.
Find the coordinates for the point on the line where x = 45.
Consider the following graph:
Complete the table of values for the line shown in the graph:
| x | 0 | 1 |
|---|---|---|
| y |
As x increases by 1, by how much does y increase?
State the values of the gradient m, and the y-intercept, c.
Hence write the equation of the line.
Find the y-value of the point on the line where x = 22.
Consider the following graph:
Complete the table of values for the line shown in the graph:
| x | 0 | 1 |
|---|---|---|
| y |
As x increases by 1, by how much does y decrease?
State the values of the gradient m, and the y-intercept, c.
Hence write the equation of the line.
Find the y-value of the point on the line where x = 27.
Consider the following graph:
As x increases by 1, by how much does y increase?
State the values of the gradient m, and the y-intercept, c.
Hence write the equation of the line.
Find the coordinates for the point on the line where x = 50.
Consider the following graph:
As x increases by 2, by how much does y decrease?
Hence as x increases by 1, by how much does y decrease?
State the values of the gradient m, and the y-intercept, c.
Hence write the equation of the line.
Find the coordinates for the point on the line where x = - 14.
For each of the following graphs:
State the coordinates of the y-intercept.
Find the gradient of the line.
Write the linear equation expressing the relationship between x and y.
Find the equation expressing the relationship between x and y, for each of the following graphs:
Consider the following graph:
Find the linear equation expressing the relationship between x and y.
Hence find the coordinates for the point on the line where x = 22.
Consider the following graph:
Find the linear equation expressing the relationship between x and y.
Find the coordinates for the point on the line where x = 25.
Find the equation of the line, given the following information:
The line has y-intercept of 4, and gradient of -3.
The line has y-intercept of -2, and gradient of 9.
The line contains the point \left(0,7\right) and has gradient of -1.
The line contains the origin and has gradient of \dfrac{3}{4}.
The line contains the origin and the point \left(1,3\right).
The line contains the origin and the point \left(1,-5\right).
The line contains the points \left(0,-5\right) and \left(1,1\right).
The line contains the points \left(0,2\right) and \left(2,6\right).