We've already learnt how to identify linear equations, which are shown graphically as straight line graphs. Now we are going to learn how to compare the features of linear equations. Linear equations are often written in gradient-intercept form which is handy because it helps us identify the gradient and $y$y-intercepts of these lines as shown below.
Let's look through some examples that compare these different features of linear equations.
In which of the following is $y$y increasing faster?
$x$x | $0$0 | $1$1 | $2$2 |
---|---|---|---|
$y$y | $3$3 | $10$10 | $17$17 |
Which of the following has the higher $y$y-intercept?
The line with a gradient of $4$4 that crosses the $y$y-axis at $\left(0,6\right)$(0,6).
The line given by the equation $y=x+4$y=x+4
For both linear relationships, consider when $y$y has a value of $46$46. Which has the smaller corresponding $x$x value?
$y=2x+32$y=2x+32
$x$x | $0$0 | $1$1 | $2$2 |
---|---|---|---|
$y$y | $6$6 | $10$10 | $14$14 |
Form and solve linear equations and inequations, quadratic and simple exponential equations, and simultaneous equations with two unknowns
Apply algebraic procedures in solving problems