Linear Relationships Flashcards
(11 cards)
What’s linear relationship? Give an example.
Where the value of one of the variables depends on the value of the other variable. On a graph it produces a straight line, such as the taxi price and the kms travelled.
What’s non-linear relationship? Give an example.
Where the effects are not proportional to their cause, such as the crime rate and the population density.
How does a linear rule increase?
By a constant amount each step. When graphed, linear rule shows a straight line.
What does the Cartesian plan consist of?
Two axes which divides the number plan into 4 quadrants.
How do I graph straight lines with intercepts?
1) Starting with the x or y intercept, let the other axes substitute to 0 (if you choose to start with y intercept, substitute x to 0)
2) Do the equation with the 0 substituted to receive the x or y intercept and repeat with the other intercept.
3) Connect the two separate coordinates through the Cartesian plane. Do not blend the two together.
How do I graph linear functions?
A rule for continuous line graphs can be written in the form of y=mx+c.
In the form y=mx+c what does m represent?
The slope of the line, aka the Gradient. This is the increase in the y value for every increase of 1 in the x value.
In the form of y=mx+c what does c represent?
The vertical intercept. This is where the line cuts through the y-axis.
What is the gradient and how doe you figure it out?
The gradient of the line is a measure of its slope. It’s a number which describes the steepness of a line. To figure the gradient you have rise (y axis) over run (x-axis).
How do I work out the equation for perpendicular lines?
Find the gradient and the y intercept (c) to rewrite the equation y=mx+c but m becomes the negative reciprocal of the gradient.
How do I work out the equation for parallel lines?
The gradient will be the same as given equation and the y intercept is needed to rewrite equation y=mx+c (at times you need to use algebra to rearrange the equation to match y=mx+c).
