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» » Writing Equations given Two Points

Writing Algebra Equations
Finding the Equation of a Line Given Two Points

We have written the equation of a line in slope intercept form and standard form. We have also written the equation of a line when given slope and a point. Now we are going to take it one step further and write the equation of a line when we are only given two points that are on that line.

This type of problem requires three steps. We must first use our information to find the slope and then use the slope and a point to find the y-intercept. REMEMBER: If I know the slope and y-intercept, then I can write an equation in slope intercept form. Once the equation is in slope intercept form, I can rewrite it in standard form if I need to.

Let's look at an example.

Example 1

writing an equation given two points

Steps for Writing an Equation Given Two Points

  • Use the slope formula to find the slope.

  • Use the slope (that you found in the step above) and one of the points to find the y-intercept.
    (Using y = mx+b, substitute x, y, and the slope (m) and solve the equation for b.)

  • Write the equation in slope intercept form using the slope and y-intercept.

  • If needed, you can then rewrite the equation in standard form as well.

Ok, now let's apply this skill to solve real world problems. Now you will have to read through the problem and determine which information gives you two points. Remember a point is two numbers that are related in some way.

NOTE: Also remember, that when identifying a point from a word problem, "time" is always the x-coordinate.

Writing Algebra Equations
Real World Problems

algebra equations
writing algebra equations given two points

And that's it! Not too bad, is it? I hope that you are learning how to recognize points, slope and y-intercepts when reading real world problems.

You've now completed the writing equations unit. You are now ready to move onto Systems of Equations.

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