Let's have a quick recap of what we know about straight lines on the Cartesian plane so far.
The values of $m$m and $b$b mean specific things. Explore for yourself what these values do by exploring on this interactive.
So what you will have found is that the $m$m value affects the gradient.
We also found that the $b$b value affects the $y$y intercept.
$y=3x$y=3x
a) What is the the gradient? The gradient is the value of the coefficient, (the number in front of the $x$x).
The gradient of this line is 3.
b) What is the $y$y-intercept? The $y$y-intercept is the value of the constant term, (the number on its own). The $y$y-intercept of this line is 0.
$y=-2x$y=−2x
$y=\frac{x}{2}-3$y=x2−3
Consider the equation $y=-1-\frac{9x}{2}$y=−1−9x2.
State the gradient of the line.
State the $y$y-value of the $y$y-intercept.
$2y=-4x+10$2y=−4x+10
First we need to rewrite it in the form or $y=mx+b$y=mx+b.
$y=-2x+5$y=−2x+5
Relate graphs, tables, and equations to linear, quadratic, and simple exponential relationships found in number and spatial patterns
Relate rate of change to the gradient of a graph
Investigate relationships between tables, equations and graphs