Line CD Passes Through Points C ( 3 , − 5 C(3, -5 C ( 3 , − 5 ] And D ( 6 , 0 D(6, 0 D ( 6 , 0 ]. What Is The Equation Of Line CD In Standard Form?A. 5 X + 3 Y = 18 5x + 3y = 18 5 X + 3 Y = 18 B. 5 X − 3 Y = 30 5x - 3y = 30 5 X − 3 Y = 30 C. 5 X − Y = 30 5x - Y = 30 5 X − Y = 30 D. 5 X + Y = 18 5x + Y = 18 5 X + Y = 18

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Introduction

In mathematics, the equation of a line is a fundamental concept that is used to describe the relationship between two variables. The standard form of a line is a specific way of writing the equation of a line that makes it easy to identify the slope and the y-intercept. In this article, we will learn how to find the equation of a line in standard form using the coordinates of two points on the line.

What is the Standard Form of a Line?

The standard form of a line is given by the equation:

Ax + By = C

where A, B, and C are constants, and x and y are the variables. The standard form of a line is also known as the general form of a line.

Finding the Slope of a Line

To find the equation of a line in standard form, we need to find the slope of the line. The slope of a line is a measure of how steep the line is. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Calculating the Slope

Let's consider two points on the line, C(3, -5) and D(6, 0). To find the slope of the line, we can use the formula:

m = (y2 - y1) / (x2 - x1)

where m is the slope, and (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the values, we get:

m = (0 - (-5)) / (6 - 3) m = 5 / 3

So, the slope of the line is 5/3.

Finding the Equation of the Line

Now that we have the slope, we can find the equation of the line in standard form. We can use the point-slope form of a line, which is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, and m is the slope.

Let's use the point C(3, -5) and the slope m = 5/3. Plugging in the values, we get:

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

To get the equation in standard form, we can multiply both sides of the equation by 3 to eliminate the fraction:

3(y + 5) = 5(x - 3) 3y + 15 = 5x - 15

Now, we can rearrange the terms to get the equation in standard form:

5x - 3y = 30

Conclusion

In this article, we learned how to find the equation of a line in standard form using the coordinates of two points on the line. We first found the slope of the line using the formula m = (y2 - y1) / (x2 - x1). Then, we used the point-slope form of a line to find the equation of the line in standard form. Finally, we rearranged the terms to get the equation in standard form.

Answer

The equation of the line CD in standard form is:

5x - 3y = 30

Q: What is the standard form of a line?

A: The standard form of a line is given by the equation Ax + By = C, where A, B, and C are constants, and x and y are the variables.

Q: How do I find the slope of a line?

A: To find the slope of a line, you can use the formula m = (y2 - y1) / (x2 - x1), where m is the slope, and (x1, y1) and (x2, y2) are the coordinates of two points on the line.

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

A: The point-slope form of a line is given by the equation y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.

Q: How do I find the equation of a line in standard form?

A: To find the equation of a line in standard form, you can use the point-slope form of a line and then multiply both sides of the equation by a constant to eliminate any fractions.

Q: What if I have two points on the line, but I don't know the slope?

A: You can use the two points to find the slope using the formula m = (y2 - y1) / (x2 - x1), and then use the point-slope form of a line to find the equation of the line in standard form.

Q: Can I use any two points on the line to find the equation?

A: Yes, you can use any two points on the line to find the equation of the line in standard form. However, it's often easier to use points that have integer coordinates.

Q: How do I know which option is correct?

A: To determine which option is correct, you can plug in the values of x and y into each option and see which one satisfies the equation.

Q: What if I get a negative value for the slope?

A: If you get a negative value for the slope, it means that the line has a negative slope. This is perfectly fine, and you can still use the point-slope form of a line to find the equation of the line in standard form.

Q: Can I use the standard form of a line to find the slope?

A: Yes, you can use the standard form of a line to find the slope. To do this, you can rearrange the equation to isolate the slope term.

Conclusion

In this article, we answered some frequently asked questions about finding the equation of a line in standard form. We covered topics such as the standard form of a line, finding the slope of a line, and using the point-slope form of a line to find the equation of a line in standard form. We also provided some tips and tricks for finding the equation of a line in standard form.

Additional Resources

  • Mathway: A online math problem solver that can help you find the equation of a line in standard form.
  • Khan Academy: A free online learning platform that offers video lessons and practice exercises on finding the equation of a line in standard form.
  • Wolfram Alpha: A online calculator that can help you find the equation of a line in standard form.