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# Lesson 6 Homework Practice: Mastering Equations in y=mx+b Form with Detailed Solutions

## Lesson 6 Homework Practice Equations In Ymxb Form Answer Key

In this article, you will learn how to write and solve equations in y=mx+b form, also known as slope-intercept form. This form is useful for writing equations of lines and graphing them. You will also find the answer key for the lesson 6 homework practice problems.

## What is y=mx+b form?

An equation in y=mx+b form is a linear equation that shows the relationship between x and y. The equation has two parts: the slope m and the y-intercept b. The slope m tells you how steep the line is and how much y changes when x changes. The y-intercept b tells you where the line crosses the y-axis, or the value of y when x is zero.

## How to write equations in y=mx+b form?

To write equations in y=mx+b form, you need to find the slope m and the y-intercept b of the line. Here are some ways to do that:

• If you are given two points on the line, (x1,y1) and (x2,y2), you can use the formula m=(y2-y1)/(x2-x1) to find the slope. Then you can use the point-slope form of the equation, y-y1=m(x-x1), and solve for y to get the slope-intercept form.

• If you are given the graph of the line, you can use the rise over run method to find the slope. Pick two points on the line and count how much you have to go up or down (rise) and how much you have to go left or right (run) to get from one point to another. The slope is the ratio of rise over run. Then you can find the y-intercept by looking at where the line crosses the y-axis.

• If you are given a word problem that describes a linear relationship, you can use the information to find the slope and the y-intercept. For example, if a car rental company charges \$20 per day plus a \$10 service fee, you can write an equation in y=mx+b form where y is the total cost, x is the number of days, m is 20 (the rate of change), and b is 10 (the initial value).

## How to solve equations in y=mx+b form?

To solve equations in y=mx+b form, you need to isolate y on one side of the equation and simplify the other side. Here are the steps:

• Identify the slope m and the y-intercept b in the equation.

• Substitute the values of m and b into the formula y=mx+b.

• If there are any parentheses, brackets, or fractions on the right side of the equation, use the order of operations to simplify them.

• If there are any terms with x on both sides of the equation, use the addition or subtraction property of equality to move them to one side.

• If there are any coefficients or constants on both sides of the equation, use the addition or subtraction property of equality to move them to one side.

• If there is a coefficient other than 1 with y, use the multiplication or division property of equality to divide both sides by that coefficient.

• Check your answer by plugging it into the original equation and simplifying both sides. They should be equal.

## Lesson 6 Homework Practice Answer Key

Here are the answers for the lesson 6 homework practice problems. You can check your work by following the steps above and using the answer key as a guide.

ProblemEquationSolution

1y=4x+1y=4x+1

2y=-3x+5y=-3x+5

3y=(1/2)x-3y=(1/2)x-3

4x 0 1 2 3y -3 -1 1 3y=2x-3

5x -4 -2 0 2y 5 -1 -7 -13y=-3x-7

6x -3 -2 -1 0y -8 -5 -2 1y=3x+1

7y=-x-4

8y=-2x-2

9y=-3x+3

10y=x-5

## Lesson 6 Homework Practice Equations In Ymxb Form Answer Key

In this article, you will learn how to write and solve equations in y=mx+b form, also known as slope-intercept form. This form is useful for writing equations of lines and graphing them. You will also find the answer key for the lesson 6 homework practice problems.

## What is y=mx+b form?

An equation in y=mx+b form is a linear equation that shows the relationship between x and y. The equation has two parts: the slope m and the y-intercept b. The slope m tells you how steep the line is and how much y changes when x changes. The y-intercept b tells you where the line crosses the y-axis, or the value of y when x is zero.

## How to write equations in y=mx+b form?

To write equations in y=mx+b form, you need to find the slope m and the y-intercept b of the line. Here are some ways to do that:

• If you are given two points on the line, (x1,y1) and (x2,y2), you can use the formula m=(y2-y1)/(x2-x1) to find the slope. Then you can use the point-slope form of the equation, y-y1=m(x-x1), and solve for y to get the slope-intercept form.

• If you are given the graph of the line, you can use the rise over run method to find the slope. Pick two points on the line and count how much you have to go up or down (rise) and how much you have to go left or right (run) to get from one point to another. The slope is the ratio of rise over run. Then you can find the y-intercept by looking at where the line crosses the y-axis.

• If you are given a word problem that describes a linear relationship, you can use the information to find the slope and the y-intercept. For example, if a car rental company charges \$20 per day plus a \$10 service fee, you can write an equation in y=mx+b form where y is the total cost, x is the number of days, m is 20 (the rate of change), and b is 10 (the initial value).

## How to solve equations in y=mx+b form?

To solve equations in y=mx+b form, you need to isolate y on one side of the equation and simplify the other side. Here are the steps:

• Identify the slope m and the y-intercept b in the equation.

• Substitute the values of m and b into the formula y=mx+b.

• If there are any parentheses, brackets, or fractions on the right side of the equation, use the order of operations to simplify them.

• If there are any terms with x on both sides of the equation, use the addition or subtraction property of equality to move them to one side.

• If there are any coefficients or constants on both sides of the equation, use the addition or subtraction property of equality to move them to one side.

• If there is a coefficient other than 1 with y, use the multiplication or division property of equality to divide both sides by that coefficient.

• Check your answer by plugging it into the original equation and simplifying both sides. They should be equal.

## Lesson 6 Homework Practice Answer Key

Here are the answers for the lesson 6 homework practice problems. You can check your work by following the steps above and using the answer key as a guide.

ProblemEquationSolution

1y=4x+1y=4x+1

2y=-3x+5y=-3x+5

3y=(1/2)x-3y=(1/2)x-3

4x 0 1 2 3y -3 -1 1 3y=2x-3

5x -4 -2 0 2y 5 -1 -7 -13y=-3x-7

6x -3 -2 -1 0y -8 -5 -2 1y=3x+1

7y=-x-4

8y=-2x-2

9y=-3x+3

10y=x-5

### How to graph equations in y=mx+b form?

To graph equations in y=mx+b form, you need to plot the y-intercept and use the slope to find another point on the line. Here are the steps:

• Identify the slope m and the y-intercept b in the equation.

• Plot the point (0,b) on the y-axis. This is the y-intercept.

• Use the slope m to find another point on the line. The slope m is the ratio of rise over run, or how much y changes when x changes by 1 unit. If m is positive, move up and to the right from the y-intercept. If m is negative, move down and to the right from the y-intercept.

• Plot the second point and draw a line through both points. This is the graph of the equation.

### Examples of graphing equations in y=mx+b form

Here are some examples of graphing equations in y=mx+b form. You can use a graphing tool or a grid paper to follow along.

• y=2x-3: The slope is 2 and the y-intercept is -3. Plot the point (0,-3) on the y-axis. Move up 2 units and to the right 1 unit from the y-intercept to find another point on the line. Plot the point (1,-1) and draw a line through both points.

• y=-3x+5: The slope is -3 and the y-intercept is 5. Plot the point (0,5) on the y-axis. Move down 3 units and to the right 1 unit from the y-intercept to find another point on the line. Plot the point (1,2) and draw a line through both points.

• y=(1/2)x-4: The slope is 1/2 and the y-intercept is -4. Plot the point (0,-4) on the y-axis. Move up 1 unit and to the right 2 units from the y-intercept to find another point on the line. Plot the point (2,-3) and draw a line through both points.

### Conclusion

In this article, you have learned how to write and solve equations in y=mx+b form, also known as slope-intercept form. You have also learned how to graph equations in y=mx+b form by using the slope and the y-intercept. You have practiced these skills by completing the lesson 6 homework problems and checking your answers with the answer key. We hope this article has helped you understand and apply the concepts of equations in y=mx+b form. b99f773239

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