The Point-slope Form Of The Equation Of The Line That Passes Through \[$(-9, -2)\$\] And \[$(1, 3)\$\] Is \[$y - 3 = \frac{1}{2}(x - 1)\$\].What Is The Slope-intercept Form Of The Equation For This Line?A. \[$y =

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Introduction

In mathematics, the slope-intercept form of a line is a fundamental concept that helps us understand the relationship between the slope and the y-intercept of a line. The slope-intercept form is a way of expressing the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept. In this article, we will explore the slope-intercept form of a line and provide a step-by-step guide on how to convert the point-slope form to the slope-intercept form.

What is the Slope-Intercept Form?

The slope-intercept form of a line is a way of expressing the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept. The slope-intercept form is a convenient way to express the equation of a line because it allows us to easily identify the slope and the y-intercept of the line.

Converting Point-Slope Form to Slope-Intercept Form

To convert the point-slope form to the slope-intercept form, we need to follow these steps:

  1. Identify the slope: The slope is the coefficient of the x-term in the point-slope form. In the given equation, the slope is 1/2.
  2. Identify the y-intercept: The y-intercept is the constant term in the point-slope form. In the given equation, the y-intercept is 3.
  3. Write the equation in slope-intercept form: Once we have identified the slope and the y-intercept, we can write the equation in slope-intercept form by multiplying the slope by x and adding the y-intercept.

Example: Converting Point-Slope Form to Slope-Intercept Form

Let's consider the given equation: y - 3 = (1/2)(x - 1). To convert this equation to slope-intercept form, we need to follow the steps outlined above.

  1. Identify the slope: The slope is the coefficient of the x-term in the point-slope form. In this equation, the slope is 1/2.
  2. Identify the y-intercept: The y-intercept is the constant term in the point-slope form. In this equation, the y-intercept is 3.
  3. Write the equation in slope-intercept form: Once we have identified the slope and the y-intercept, we can write the equation in slope-intercept form by multiplying the slope by x and adding the y-intercept.

y - 3 = (1/2)(x - 1) y - 3 = (1/2)x - 1/2 y = (1/2)x + 3 - 1/2 y = (1/2)x + 5/2

Conclusion

In conclusion, the slope-intercept form of a line is a fundamental concept in mathematics that helps us understand the relationship between the slope and the y-intercept of a line. By following the steps outlined above, we can convert the point-slope form to the slope-intercept form. The slope-intercept form is a convenient way to express the equation of a line because it allows us to easily identify the slope and the y-intercept of the line.

Final Answer

Q: What is the slope-intercept form of a line?

A: The slope-intercept form of a line is a way of expressing the equation of a line in the form y = mx + b, where m is the slope and b is the y-intercept.

Q: What is the slope in the slope-intercept form?

A: The slope in the slope-intercept form is the coefficient of the x-term, which is the number that is multiplied by x.

Q: What is the y-intercept in the slope-intercept form?

A: The y-intercept in the slope-intercept form is the constant term, which is the number that is added to the product of the slope and x.

Q: How do I convert the point-slope form to the slope-intercept form?

A: To convert the point-slope form to the slope-intercept form, you need to follow these steps:

  1. Identify the slope: The slope is the coefficient of the x-term in the point-slope form.
  2. Identify the y-intercept: The y-intercept is the constant term in the point-slope form.
  3. Write the equation in slope-intercept form: Once you have identified the slope and the y-intercept, you can write the equation in slope-intercept form by multiplying the slope by x and adding the y-intercept.

Q: What is the difference between the slope-intercept form and the point-slope form?

A: The slope-intercept form and the point-slope form are two different ways of expressing the equation of a line. The slope-intercept form is a more general form that can be used to express the equation of any line, while the point-slope form is a more specific form that is used to express the equation of a line that passes through a given point.

Q: Can I use the slope-intercept form to find the equation of a line that passes through two points?

A: Yes, you can use the slope-intercept form to find the equation of a line that passes through two points. To do this, you need to follow these steps:

  1. Find the slope: Use the two points to find the slope of the line.
  2. Find the y-intercept: Use one of the points and the slope to find the y-intercept.
  3. Write the equation in slope-intercept form: Once you have found the slope and the y-intercept, you can write the equation in slope-intercept form.

Q: How do I use the slope-intercept form to graph a line?

A: To use the slope-intercept form to graph a line, you need to follow these steps:

  1. Identify the slope and the y-intercept: Use the slope-intercept form to identify the slope and the y-intercept.
  2. Plot the y-intercept: Plot the y-intercept on the y-axis.
  3. Use the slope to find another point: Use the slope to find another point on the line.
  4. Draw the line: Draw a line that passes through the two points.

Q: Can I use the slope-intercept form to find the equation of a line that is parallel to another line?

A: Yes, you can use the slope-intercept form to find the equation of a line that is parallel to another line. To do this, you need to follow these steps:

  1. Find the slope of the given line: Use the slope-intercept form to find the slope of the given line.
  2. Use the slope to find the equation of the parallel line: Use the slope-intercept form to find the equation of the parallel line.

Conclusion

In conclusion, the slope-intercept form of a line is a fundamental concept in mathematics that helps us understand the relationship between the slope and the y-intercept of a line. By following the steps outlined above, we can convert the point-slope form to the slope-intercept form and use the slope-intercept form to find the equation of a line that passes through two points, graph a line, and find the equation of a line that is parallel to another line.