Equations and graphs
Consider this table of values of and .
Notice that for every increase of in the the increases by . This constant difference shows that there is a linear relationship between and . If we plot the values on the axes we get the straight line in the graph above.
The gradient of the line is . The gradient of any line can be calculated using the formula rise over run (either by reading off the graph or using any two coordinates from the table).
e.g. Point 1: $latex(1,30)$ and Point 2:
Straight line equations
The general form of a straight line is
Where is the gradient of the line and is the intercept (i.e. where the line crosses the axis).
This form is handy for sketching a line and for reading off the gradient.
e.g. Sketch the line
The and the
Note that sometimes we need to rearrange an equation into the form .
e.g. Find the gradient and y intercept of the line
The line will cut the axis at with a gradient of .
Use the desmos online calculator to draw different straight lines to understand the relationship between the equation and the graph.
Gradient = 0
Gradient = undefined
The gradient of parallel lines are equal.
Tables and graphs activity
Complete the following interactive activity