Look for and express regularity in repeated reasoning. Launch 10 minutes Two-Step Equations Opener: As students enter the room, they will immediately pick up and begin working on the opener — Instructional Strategy - Process for openers. This method of working and going over the opener lends itself to allow students to construct viable arguments and critique the reasoning of others, which is mathematical practice 3.
Writing Linear Equations Given Slope and a Point When you are given a real world problem that must be solved, you could be given numerous aspects of the equation. If you are given slope and the y-intercept, then you have it made. You have all the information you need, and you can create your graph or write an equation in slope intercept form very easily.
However, most times it's not that easy and we are forced to really understand the problem and decipher what we are given. It could be slope and the y-intercept, but it could also be slope and one point or it could be just two points.
If you are given slope and a point, then it becomes a little trickier to write an equation. Although you have the slope, you need the y-intercept. You have enough information to find the y-intercept, but it requires a few more steps.
Let's look at an example.
You must always know the slope m and the y-intercept b. Writing Equations Given Slope and a Point Write the equation of a line, in slope intercept form, that passes through the point 6, -3 with a slope of Let's first see what information is given to us in the problem. We'll record this information in the chart below to keep it organized.
Notice that in the chart, the 2 grey sections slope and y-intercept are the two numbers that we need in order to write our equation. We know the slope and a point x,y.
We can use this information to solve for b. Then we can write our equation. Then you will solve for b. Now we know the slope m is -2 because that was given to us. We also now know the y-intercept bwhich is 9 because we just solved for b.
We can now write our equation! Since you are so awesome at solving equations, I'm sure this wasn't too painful. Now let's look at a real world applications of this skill. Here you will have to read the problem and figure out the slope and the point that is given.
The slope is going to be your "rate" and the point will be two numbers that are related in some way.
Write a linear equation that can be used to determine the cost of a cab ride to anywhere around Washington DC. Let's think about what we know in this problem. I know that this is a rate and therefore, is also the slope. These two numbers are related.
This relation means that we know the x and y coordinates of an ordered pair. Now we know the slope m is 1. We also now know the y-intercept bwhich is 3 because we just solved for b. Once you have m slope and b y-interceptyou can write an equation in slope intercept form.
Now you are ready to solve real world problems given two points. It's not the hard - I promise.Equation of a Line from 2 Points. First, let's see it in action. Here are two points (you can drag them) and the equation of the line through them.
This lesson also goes right into the application of two step equations (mathematical practices 2/4) - students will apply equations to area and perimeter, and set up and solve equations for real world problems. The biggest problem I run into with this lesson is students using the wrong sign when performing inverse operations - for example if you have 2x - 5, students will want to subtract 5.
Improve your math knowledge with free questions in "Solve two-step equations" and thousands of other math skills.
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. Students learn to write a sentence as an equation. For example, "Twice a number increased by 5 is 21" can be written as 2n + 5 = Next, solve the equation by subtracting 5 from both sides, to get 2n = 16, then divide both sides by 2, to get n = 8.
Learn how to construct and solve a basic linear equation to solve a word problem.