HA1-394 Slope Intercept and Standard Form Ax + By = C - No Fractions, get rid of them!! - Variable A must ALWAYS be positive. In this presentation, you will see examples of linear equations converted into standard form and into slope intercept form. Standard form is Ax + By = C where there can be no fractions and A MUST ALWAYS BE POSITIVE. Slope intercept form is y=mx+b, where m is the slope and b is the y intercept.

Changing a linear equation into Standard Form Feel free to try on your own before you click. See if you’re getting it!! Changing a linear equation into Standard Form Change y = 3x +6 into standard form. Step 1: Move the x term to the left side. Step 2: Make sure that the x-term has a positive co-efficient. Work: y = 3x + 6 -3x -3x -3x + y = 6 -1(-3x + y = 6) Final Answer: 3x – y = -6 Try these problems on your own before you go to the next slide. Practice problems: 1. y = 4x – 7 2. y = -2x +1 Note: We multiply by -1 to get A positive. Multiplying by -1 has the effect of changing all the signs of ALL terms.

Now onto converting linear equations into Practice problems: 1. y = 4x – 7 -4x -4x -4x + y = -7 -1(-4x + y = -7) Final Answer: 4x – y = 7 2. y = -2x +1 +2x +2x 2x + y = 1 Final Answer: 2x + y = 1 Now onto converting linear equations into standard form ( Ax + By =C) with fractional coefficients!! How do we KNOW it’s our final answer. Look, it’s in Ax+By=C form, A is positive, and we have NO fractions. That makes GOOD standard form!

Convert to Standard form if the linear equation has fractions in it. Note: Let's get rid of fractions first because we know we will have to do it later, AND it makes moving terms easier. So, we will get rid of fractions, then get our x term on the left, then make sure the x term is positive. Example #1 y = 3/4x + ½ 4(y = 3/4x + ½) 4y = 3x + 2 -3x -3x -3x + 4y = 2 -1( -3x + 4y = 2) Final Answer: 3x – 4y = -2 Feel free to try on your own before you click. See if you’re getting it!! Getting Rid of Fractions! LOOK: We chose 4 as the multiplier because multiplying each term by 4 will get rid of all fractions. 4 is the LCM of the denominators 2 and 4 Brush up on fraction multiplication. 4(3/4) becomes 4 x 3 = 12 = 3 = 3 1 4 4 1 You multiply across the top and bottom and get 3 in the end after reductions. This is where the 3x comes from. 4 ( ½) = 2. Note: We multiply by -1 to get A positive. Multiplying by -1 has the effect of changing all the signs of ALL terms.

Example #2 Y = -4/5x – 2/3 15(Y = -4/5x – 2/3) 15Y = -12x – 10 Note: Let's get rid of fractions first because we know we will have to do it later, AND it makes moving terms easier. So, we will get rid of fractions, then get our x term on the left, then make sure the x term is positive. Example #2 Y = -4/5x – 2/3 15(Y = -4/5x – 2/3) 15Y = -12x – 10 +12X +12x 12X + 15y = -10 Final Answer: 12x + 15y = -10 Now, you try these 2 problems before you go to next slide. 1. y = 2/3x – 1/7 2. y = -3/4x + 1/3 Look!! We choose 15 because it is the smallest number that 5 AND 3 go into evenly ( it is the LCM of 5 and 3), and when we crunch our fractions, we will get whole number coefficients to go with our variables. (The # beside the variable is the coefficient) Brush up on fraction multiplication. 15(-4/5) becomes 15 x -4 = -60 = -12 = -12 1 5 5 1 You multiply across the top and bottom and get -12 in the end after reductions. This is where the -12x comes from. 15 (-2/3) = -30/3 = -10. How do we KNOW it’s our final answer. Look, it’s in Ax+By=C form, A is positive, and we have NO fractions. That makes GOOD standard form!

Problem #1 1. y = 2/3x – 1/7 21(y = 2/3x – 1/7) 21Y = 14x – 3 Note: Let's get rid of fractions first because we know we will have to do it later, AND it makes moving terms easier. So, we will get rid of fractions, then get our x term on the left, then make sure the x term is positive. Problem #1 1. y = 2/3x – 1/7 21(y = 2/3x – 1/7) 21Y = 14x – 3 -14x -14x -14x + 21y = -3 -1(-14x + 21y = -3) Final Answer: 14X – 21y = 3 Brush up on fraction multiplication. 21(2/3) = 42/3 = 14 Shortcut: When you multiply a WHOLE # times a fraction, the whole number gets multiplied by the top of the fraction, and then you divide by the denominator of the fraction. 21(-1/7) = -21/7 = -3. Look!! We choose 21 because it is the smallest number that 3 AND 7 go into evenly ( it is the LCM of 7 and 3), and when we crunch our fractions, we will get whole number coefficients to go with our variables. (The # beside the variable is the coefficient)

Now, onto getting into slope intercept formula. Note: Let's get rid of fractions first because we know we will have to do it later, AND it makes moving terms easier. So, we will get rid of fractions, then get our x term on the left, then make sure the x term is positive. Problem #2 2. y = -3/4x + 1/3 12(y = -3/4x + 1/3 ) 12y = -9x + 4 +9x +9x 9X + 12y = 4 Final Answer: 9X + 12y = 4 Now, onto getting into slope intercept formula. Look!! We choose 12 because it is the smallest number that 4 AND 3 go into evenly ( it is the LCM of 4 and 3), and when we crunch our fractions, we will get whole number coefficients to go with our variables. (The # beside the variable is the coefficient)

Convert Linear Equations into Slope Intercept Form ( y= mx + b ) - CAN have Fractions! - Any numbers( coefficients) can be positive or negative. Why do we get equations into slope intercept form? It helps rapidly graph lines by giving us the slope ( m ) and the y intercept ( b ). Steps: Move x term to the right. Get y by itself by dividing. Make sure y is positive. Make sure you're in y = mx + b. 3x – 4y = 1 -3x -3x - 4y = -3x + 1 -4y = -3x + 1 -4 -4 y = 3/4x - ¼ Final Answer : y = -3/4x – ¼ with slope (m) of -3/4 and y intercept (b) of -1/4th Now you try a couple before you go to the next slide. Convert to slope intercept form. 1. 5x + 3y = 15 2. 4x – y = 12 Convert Linear Equations into Slope Intercept Form ( y= mx + b ) Feel free to try to switch to y=mx+b form on your own before you click. See if you’re getting it!! Basically this means solve for y or get y by itself using inverses. TIP!! -3/-4 is the same as positive ¾ because you’re dividing a negative by a negative, which ALWAYS makes a positive. LOOK!! When you divide the right side by -4, each term on that side gets divided by -4. Don’t forget to divide the constant by -4 here.

Steps: Move x term to the right. Get y by itself by dividing Steps: Move x term to the right. Get y by itself by dividing. Make sure the y coefficient is positive. Make sure you're in y = mx + b. Practice problem #1 5x + 3y = 15 -5x -5x 3y = -5x + 15 3 3 y = -5/3x + 5 Final Answer: Y = -5/3x + 5 with slope ( m) of -5/3 and y intercept ( b) of 5

4x – y = 12 -4x -4x -y = -4x + 12 -1(-y = -4x + 12) y = 4x – 12 Steps: Move x term to the right. Get y by itself by dividing. Make sure y is positive. Make sure you're in y = mx + b. Practice problem #2 4x – y = 12 -4x -4x -y = -4x + 12 -1(-y = -4x + 12) y = 4x – 12 Final Answer: y = 4x – 12 with slope ( m ) of 4 ( or 4/1 if you need to use rise over run) and a y intercept ( b) of -12. Now go pass that QUIZ !!!!!!!!!!!!!!!!!!!