Learn

Linear Equations

Writing Linear Equations

You will learn how to write an equation of a line given certain information: point and slope and two points

Formulas:

slope = rise/run

m = [(ysub2 - ysub1)/(xsub2 - xsub1)]

Slope intercept form: y = mx + b where m = slope, b = y-intercept

Slope Intercept Form

Given point and slope Our first objective will be to write an equation of line in slope intercept form when we know the slope of the line and one point on that line. Before you learn how to do this algebraically let’s look at how to graph the line with this given information. Graph point first then slope.

Example #1

Open Write the Equation of a Line in Slope-Intercept Form Given the Slope and a Point on the Line in a new tab

Finding the Equation Algebraically

As you can see, it is difficult to see exactly where the line crosses the y-axis without doing a little guessing. This will be a time where you will have to find the equation of the line algebraically. Also, you may prefer to do it algebraically because of the time that it can take to graph the equation.

The graph of a line on a coordinate plane; the line has a negative slope

Example #2

Open Write the Equation of a Line in Slope-Intercept Form Given the Slope and a Point on the Line in a new tab

Equations Given Two Points

The second objective of this lesson is to write an equation of a line in slope intercept form given two points on the line. Let’s work an example together. The problem is to write the equation of a line that goes through the points (-1, 1) and (1, -3).

Example #3

Open Find the Equation of a Line in Slope-Intercept Form Given Two Points in a new tab

Example #4

Open Find the Equation of a Line in Slope-Intercept Form Given Two Points in a new tab