linear functions application
For y = 2x + 5, we say that y is a function of x Recall, that f(x) is read ”f of x”, and we say that f is a function of x.Definition. A linear function is a function on the form,
y = f(x) = mx + b
where m is the slope of the line and b is the y-intercet. We call x the independent variable and y the dependent variable. KEY POINTS
Interpret constant rate of changes problems as applications of the slope of a linear function.
If you know a real-world problem is roughly linear, such as the distance you travel when you go for a jog, all you need is two points and you can graph the function and make some assumptions as to what happens beyond the two points, so long as you maintain the same rate.
The slope of a function is the same as the rate of change for the dependent variable. For instance, if you're graphing distance vs. time, then the slope is how fast your distance is changing with time, or in other words, your speed.
When checking where two linear functions intersect, set them equal to each other and solve for the dependent variable, x.
slope
The ratio of the vertical and horizontal distances between two points on a line; zero if the line is horizontal, undefined if it is vertical.
linear equation
A polynomial equation of the first degree (such as x = 2y - 7).
