Writing equations of lines

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So, before we get into the equations of lines we first need to briefly look at vector functions. At this point all that we need to worry about is notational issues and how they can be used to give the equation of a curve. The best way to get an idea of what a vector function is and what its graph looks like is to look at an example.

Writing equations of lines

So, consider the following vector function. Note as well that a vector function can be a function of two or more variables. However, in those cases the graph may no longer be a curve in space. The vector that the function gives can be a vector in whatever dimension we need it to be. So, to get the graph of a vector function all we need to do is plug in some values of the variable and then plot the point that corresponds to each position vector we get out of the function and play connect the dots.

Here are some evaluations for our example. If we do some more evaluations and plot all the points we get the following sketch. In this case we get an ellipse.

In the last lesson, I showed you how to get the equation of a line given a point and a slope using the formula. Anytime we need to get the equation of a line, we need two things. Lead Student Lesson Plan L Using Slopes and Writing Equations of Lines Main Purposes • Discuss the BYU-Pathway Worldwide devotional • Practice speaking English: Getting better at the skills listed below will help all students to be more readily understood when they speak English with others. Tutorial Equations of Lines. WTAMU > Virtual Math Lab > College Algebra. Learning Objectives. In this tutorial we will look closer at equations of straight lines. We will be going over how to come up with our own equations given certain information. This website helps you with writing linear equations.

It is important to not come away from this section with the idea that vector functions only graph out lines. Okay, we now need to move into the actual topic of this section.

In this case we will need to acknowledge that a line can have a three dimensional slope. So, we need something that will allow us to describe a direction that is potentially in three dimensions.

We already have a quantity that will do this for us.

Vectors give directions and can be three dimensional objects. We now have the following sketch with all these points and vectors on it. It can be anywhere, a position vector, on the line or off the line, it just needs to be parallel to the line.

There are several other forms of the equation of a line.Writing Equations in Slope Intercept Form. Let's first quickly review slope intercept form.

Equations that are written in slope intercept form are the easiest to graph and easiest to write given the proper information. All you need to know is the slope (rate) and the y .

Graphing Vertical and Horizontal Lines i. The preceding methods will not work for equations in the form x = a or y = b. ii. Vertical Lines 1. Equation: x = a 2. The graph is a line parallel to the y-axis and passes through the x Graphing and Writing Linear Equations.

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Header Button Label: Get Started Now Get Started Header Button Label: View writing samples View writing samples. Writing Equations of Perpendicular and Parallel Lines Write an equation of the line that passes through (3, 2) and is (a) perpendicular and (b) parallel to the line y = º3 x + 2.

write the equations of the lines, including the start and stop points for each line. Alternatively, have students program their designs, using software or graphing calculators. Strategies for Differentiation Writing equations of lines Keywords.

In this writing equations and lines worksheet, students solve and complete 22 various types of problems. First, they write an equation of the line through the points and with the slope as stated in each.