05/14 5. Linear Functions and Models Free Online FlashCards

What is a linear function?

A linear function has a straight-line graph and can be written as $f(x)=mx+b$, where $m$ is the slope and $b$ is the y-intercept.

What do the parameters mean in a linear model?

In $y=mx+b$, $m$ is the rate of change and $b$ is the initial value when the input is zero.

What does slope measure?

The slope is the constant rate of change: $m=\frac{\Delta y}{\Delta x}$. It measures vertical change per unit of horizontal change.

How do you calculate slope from two points?

For $(x_1,y_1)$ and $(x_2,y_2)$, use $m=\frac{y_2-y_1}{x_2-x_1}$, with $x_1\ne x_2$.

How does slope determine graph direction?

If $m>0$, the function is increasing; if $m<0$, it is decreasing; and if $m=0$, it is constant.

What are the special cases for line slope?

A horizontal line has slope $0$. A vertical line has undefined slope because its horizontal change is zero.

How do you identify the y-intercept?

The y-intercept is $(0,b)$, found by setting $x=0$ in $y=mx+b$.

How do you find the x-intercept?

Set $y=0$ and solve for $x$. The resulting point is the x-intercept, also called the zero of the function.

What is point-slope form?

Point-slope form is $y-y_1=m(x-x_1)$. It is useful when a line’s slope and one point are known.

What is standard form for a line?

Standard form is $Ax+By=C$, usually with integer coefficients and often with $A>0$.

How do you graph $y=mx+b$?

Plot the y-intercept $(0,b)$, use the slope as rise over run to plot more points, then draw the line through them.

What is a piecewise function?

A piecewise function uses different formulas on different parts of its domain; each formula applies only when its condition is satisfied.