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All Common Core: High School - Algebra Resources

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Flashcards: Rearrange Formulas and Solve Equations: CCSS.Math.Content.HSA-CED.A.4

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for y_2 .

y_2=x_2-x_1m+y_1

y_2=(x_2-x_1)m

y_2=x_2m-x_1+y_1

y_2=(x_2-x_1)+y_1m

y_2=(x_2-x_1)m+y_1

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Flashcards: Rearrange Formulas and Solve Equations: CCSS.Math.Content.HSA-CED.A.4

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for y_2 .

Your answer:

y_2=x_2-x_1m+y_1

Your answer:

y_2=(x_2-x_1)m

Your answer:

y_2=x_2m-x_1+y_1

Your answer:

y_2=(x_2-x_1)+y_1m

Correct answer:

y_2=(x_2-x_1)m+y_1

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically y_2 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next, add y_1 to both sides of the equation.

$\\(x_2-x_1)m+y_1=y_2-y_1+y_1 \\(x_2-x_1)m+y_1=y_2$

Therefore, the equation solved for y_2 is

y_2=(x_2-x_1)m+y_1

Flashcards: Rearrange Formulas and Solve Equations: CCSS.Math.Content.HSA-CED.A.4

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for y_1 .

y_1=-(x_2-x_1)m-y_2

y_1=(x_2-x_1)m+y_2

y_1=-(x_2-x_1)m+y_2

y_1=-(x_2-x_1)m+y_2m

y_1=(x_2-x_1)m-y_2

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Flashcards: Rearrange Formulas and Solve Equations: CCSS.Math.Content.HSA-CED.A.4

To calculate the slope of a line, the following formula is used.

$m=\frac{y_2-y_1}{x_2-x_1}$

Solve this equation for y_1 .

Your answer:

y_1=-(x_2-x_1)m-y_2

Your answer:

y_1=(x_2-x_1)m+y_2

Your answer:

y_1=-(x_2-x_1)m+y_2m

Your answer:

y_1=(x_2-x_1)m-y_2

Correct answer:

y_1=-(x_2-x_1)m+y_2

Explanation:

This question is asking to rearrange the slope formula to highlight a quantity of interest, specifically y_1 .

To rearrange the formula, perform algebraic operations. Recall that whatever operation that is done to one side needs to also be done on the other side in order to keep the equation balanced.

First, multiply both sides by the quantity (x_2-x_1) in order to move it from the right side of the equation to the left side. Performing the opposite operation allows for rearranging to occur.

$\\(x_2-x_1)\cdot m=\frac{y_2-y_1}{x_2-x_1}\cdot (x_2-x_1) \\\\(x_2-x_1)m=y_2-y_1$

Next, subtract y_2 to both sides of the equation.

$\\(x_2-x_1)m-y_2=y_2-y_1-y_2 \\(x_2-x_1)m-y_2=-y_1$

Now, divide by negative one on both sides.

$\frac{(x_2-x_1)m-y_2}{-1}=-\frac{y_1}{-1}$

-(x_2-x_1)m+y_2=y_1

Therefore, the equation solved for y_1 is,

y_1=-(x_2-x_1)m+y_2

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All Common Core: High School - Algebra Resources

Flashcards: Rearrange Formulas and Solve Equations: CCSS.Math.Content.HSA-CED.A.4

Flashcards: Rearrange Formulas and Solve Equations: CCSS.Math.Content.HSA-CED.A.4

Flashcards: Rearrange Formulas and Solve Equations: CCSS.Math.Content.HSA-CED.A.4

Flashcards: Rearrange Formulas and Solve Equations: CCSS.Math.Content.HSA-CED.A.4

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