Writing+Equations+of+Lines+-+Part+1

When we write the equation of the line, we write it in **slope-intercept form**.

Slope-intercept form is the "formula" we use to write the equation of a line. It looks like this: y = mx + b
 * What is slope-intercept form?**

Each part of the equation has a specific meaning. The "m" represents the slope of the line. The "b" represents the y-intercept of the line. The "x" and "y" represent the coordinates of any point on the line (x,y).

When we write an equation out in slope-intercept form, we need to substitute numbers in for "m" (the slope) and "b" (the y-intercept). This is why this form is called //slope// - //intercept// form. The "x" and "y" will stay as variables. For example:

y = 3x + 7

y = (-1/2)x - 4

**TASK: What two things do we need to have in order to write the equation of a line in slope-intercept form?**

There are three different scenarios on the Regents in which you will be asked to write an equation in slope-intercept form. In this lesson, we will talk about two of those situations:
 * How do we write equations in slope-intercept form?**

1. When you're given the slope and the y-intercept 2. When you're given the slope and another point on the line (not the y-intercept)

Since the only two things we need to know to write the equation of the line in slope-intercept form are //the slope// and //the y-intercept//, if they're both given to you, you can SUBSTITUTE them into the equation y = mx + b
 * When you're given the slope and the y-intercept:**

For example: Write the equation in slope-intercept form of the line that has a slope of -2 and a y-intercept of 7.

Based on what's given in the problem, we know that m = -2 and b = 7. Therefore, we can substitute them into y = mx + b and we get: y = -2x + 7.

Example: Find the equation of the line that has a slope of 2/3 and goes through the point (-3,1)
 * When you're given the slope and another point on the line:**

The two things we need to write the equation of a line in slope-intercept form are the SLOPE and the Y-INTERCEPT. One of these things (the slope) is given to us in this problem. Then, we need to use the other information given in the problem to find the y-intercept.

So far, we know that m = 2/3. We need to find "b." The other information given (-3,1) is another point on the line and we can substitute them in for "x" and "y." We get:

y = (2/3)x + b --> Substitute 2/3 in for "m" 1 = (2/3)(-3) + b --> Substitute 1 in for "y" and -3 in for "x". These numbers come from the (x,y) from the point given (-3,1). 1 = -2 + b --> Simplify by multiplying 2/3 and -3 3 = b --> Simplify by adding 2 on both sides

Now we know what "b" is and what "m" is. m = 2/3 and b = 3. Using this information, we can write the equation of the line and we get:

y = (2/3)x + 3


 * Note: If "b" is a negative number, we would write -- instead of + in the equation.**

**TASK: Complete the four practice Regents problems below. Please SHOW ALL YOUR WORK.**

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