25+Writing+Equations+in+Slope-Intercept+Form+I

Section 5-3  **//25.//** **//__Writing Equations in Slope- Intercept Form 1__//** **__Finding Slope- Intercept Form from Two Points__** Slope- Intercept Formula: **y = mx + b** **STEP 1: Plug the slope (m) into the formula y = mx + b ** **STEP 2: Plug the y- intercept (b) into the same formula** **Example One:** m = - 3, b = 5 To write this equation in slope- intercept form, - 3 is plugged in for m and 5 is plugged in for b.  y = mx + b  y = - 3x + 5 **Example Two:** m = 4, b = - 1 To write this equation in slope- intercept form, 4 is plugged in for m and -1 is plugged in for b.  y = mx + b  y = 4x – 1 **Example Three:** m = ½, b = - 9 To write this equation in slope – intercept form, ½ is plugged in for m and – 9 is plugged in for b.  y = mx + b  y = ½x – 9 **Example Four:** m = 0, b = 4 To write this equation in slope- intercept form, 0 is plugged in for m and 4 is plugged in for b. However, because **anything multiplied by 0 is 0**, the x would become 0. This leaves you with y = 4, which happens to be a horizontal line. y = mx + b  y = 0x + 4 y = 4 **Example Five:** m = 2, b = 0 To write this equation in slope- intercept form, 2 is plugged in for m and 0 is plugged in for b. There is no need to have + 0 in the equation, therefore it is y = 2x. y = mx + b y = 2x + 0 y = 2x 
 * Writing Equations In Slope-Intercept Form Of The Line Passing Through Each Pair Of Points:**

Example 1: (1,3) (-3,-5)

1. Find Slope Of The Given Coordinates: __ 1+3__ = __4__ = __2__ -3+5 2 1

2. Plug Slope Into Equation: y=mx+b y=2x+b

3. Pick One Pair Of Coordinates To Plug In For The Values Of X & Y (1,3) or (-3,-5)

4. Find The Value Of The Y-Intercept y=2x+b 3=2(1)+b 3=2+b 1=b

5. Write The Equation Out With The Value Of The Slope And The Y-Intercept Filled In y=2x+1

Example 2: (2,1) and (3,6)

1. __2-3__=-__1__=__1__ 3-6 -3 3

2. y=mx+b y=1/3x+b

3. (2,1) or (3,6)

4. y=1/3x+b 6=1/3(3)+b 6=1+b 5=b

5. y=1/3x+5

Example 3: (-3,2) and (3,-6)

1. __-3-3__ = __-6__ = __-3__ 2+6 8 4

2. y=mx+b y=-3/4x+b

3. (-3,2) or (3,-6)

4. -6=-3/4(3)+b -6=-9/4+b -8 ¼=b

5 y=-3/4x-8 ¼

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To find the equation for a line in slope intercept that has a slope of 4 and passes though points (-1,-6), you will need to use the formula y=m(x)+b

When doing this, the slope that you are given will be used as the (m) in the equation. The two points will be used as (x) and (y) in the equation.

Ex: Write the equation of a line in slope intercept form if the line has a slope of 4 and passes through the points (-1, -6)

Start with the equation y=m(x)+b

Then plug in the points: 4=m, -1=x, and -6=y

After you plug in the numbers for the letters your equation should look like this: -6=4(-1)+b Next multiply 4*(-1)

After you do the math the equation should be: -6=-4+b

Next you need to get all similar variables on the same side of the equation. This means that you need to get (-4) on the same side as (-6).

To that you will need to add 4 to both sides. Remember that what ever is done to one side of the equation needs to be done to the other side as well.

When you add 4 the equation should now have -6 and 4 on one side and (b) on the other: -6+4=b

Next add -6 and 4 this will show you what (b) equals: -2=b

Since you have found what (b) equals you can plug it in to the equation. The equation NEEDS to be in slope intercept.

So the answer to the problem is: y=-1-2

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Good Luck!