2.3 Linear Functions

We want to be able to create equations whose solution set is a line. One tool we’ll use to do this is slope.

So now that we know what slope is, we find that the slope between to points (x_1,y_1) and (x_2,y_2) is M=\frac{y_2-y_1}{x_2-x_1}

Using slope we can now come up with an equation for a line, provided we have a point on the line and its slope.

Here is a worksheet to practice using the point-slope form of the equation of a line.

To have a unified way of writing lines, we often solve for y, and get what is known as slope intercept form of the line.

We need to be able to convert between the forms of a line.

Once in slope-intercept form, its easier to graph lines.

Here’s a worksheet you can practice graphing lines in slope-intercept form with.

Then we discovered that if two lines have slope m_1 and m_2 then they are parallel if m_1=m_2, that is they had the same slope, and they are perpendicular if m_1=-\frac{1}{m_2}

We can use these facts to figure out the equations of perpendicular and parallel lines.

Here is some extra practice for parallel and perpendicular lines.