Writing+Equations+of+Lines+-+Part+2

As discussed in the last lesson, you will see three different types of problems on the Regents that ask you to write the equation of a line. We already discussed two of them (if you're given the slope and the y-intercept OR if you're given the slope and another point on the line). In this lesson, we will discuss the third possibility - if you're **given two points on the line.**

**TASK: What are the two things you must know in order to write the equation of a line in slope-intercept form?**

In the last lesson, you were always given one or both of the things we need to know. Sometimes, we won't be given either piece of information and we'll have to figure them both out using the information that is given. For example:

Write the equation of the line that passes through the points (2, 5) and (-3, 0).

First, we find the slope using the methods we learned in the lesson on slope. We can either use the slope formula or we can graph the points and count the rise and run on the coordinate plane. Using the slope formula, we get:



Now that we know the slope, we need to determine the y-intercept (or "b"). We can use one of the methods we learned in the previous lesson because now we know the slope of the line and we're given another point on the line to substitute in for "x" and "y." We are given two points in the problem. We can choose //either point// to substitute in. We'll get the same answer either way.

We know so for that:

y = 1x + b

We can substitute in for "x" and "y" and we get:

5 = 1(2) + b 5 = 2 + b 3 = b

Now we know "m" and "b" and we can put them together to get:

y = 1x + 3 OR simply, y = x + 3

Here's another **example:**

Write the equation of the line that passes through the points (6, -2) and (-6, -6).

First, find the slope:



Then, substitute in and find the y-intercept:



Now that we know the slope and y-intercept, we can write the equation:



**TASK: How do you write the equation of a line in slope-intercept form when you're only given two points on the line?** **TASK: Complete the practice problems below. PLEASE SHOW ALL YOUR WORK.**

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