What is a Linear Function?

This video shows examples of changing constants in graphs of functions using linear equations.

Changing Constants in Graphs of Functions: Linear Functions

Linear Functions

The slope intercept form of a linear equation is y equals mx plus b. Where the constants are the m and the b. The x and the y are the variables. m stands for slope, while the b is the y intercept.

The slope of a linear equation is how steep or flat the graph is, or how steep or flat the line is. Here we have three different graphs. The first graph and the last graph have the same slope, the slope is one, since the coefficient of x is one.

This is actually the parent function of a linear equation y equals x. When your slope is positive, like it is in the first and the last graph, then the line increases from left to right. The second graph the slope is negative, negative 1/4. The line is decreasing now from left to right.

If the slope is negative, the line is decreasing from left to right. Positive slope increasing, negative slope decreasing. You may also notice that this line is not as steep as the first and the last. The greater the absolute value of the slope the steeper the line is.

The absolute value of this slope, negative 1/4, would be positive 1/4 and a fourth is less than one, which is why this line is not as steep as these lines are in the first and the last graph. b again is the y intercept, which means that’s where your line crosses the y axis.

This is the y axis here, x axis, y axis, x axis, y axis, x axis. In the first and second graph the y intercept is zero. There is no y intercept there which is why it’s crossing the y axis at zero, the origin, for both of these graphs.

However, in this third graph the y intercept is 2 which is why this graph has been shifted up two places to intercept the y axis at 2.

That’s really what the y intercept is it’s a vertical shift up or down on the y axis. If our y intercept was negative 4 then the graph of our line would go right through this point right here at negative 4. That’s how the slope and y intersect affect a linear graph.