Finding the Slope of Line G

Oct 13, 2025 by windailys.com 37 views

Introduction

In mathematics, the slope-intercept form of a line is a way to express the equation of a line in the form y = mx + b, where m is the slope of the line and b is the y-intercept. When we are given a line and asked to find the equation of a line that is perpendicular to it, we need to find the slope of the perpendicular line and then use it to find the equation of the line.

Finding the Slope of Line G

To find the slope of line G, we need to know its equation. However, since we are not given the equation of line G, we will assume that it is in the slope-intercept form y = mx + b. Let's call the slope of line G "m". The slope of a line is a measure of how steep it is, and it is calculated as the ratio of the vertical change (rise) to the horizontal change (run).

Finding the Slope of the Perpendicular Line

The slope of the perpendicular line is the negative reciprocal of the slope of line G. This means that if the slope of line G is m, then the slope of the perpendicular line is -1/m. To find the slope of the perpendicular line, we need to know the slope of line G.

Finding the Equation of the Perpendicular Line

Now that we have the slope of the perpendicular line, we can use it to find the equation of the line. We are given that the line passes through the point (4, 2). We can use this point and the slope of the line to find the equation of the line.

Step 1: Write the Equation of the Line in Slope-Intercept Form

The equation of the line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept. We know that the slope of the line is -1/m, but we don't know the value of m. We also know that the line passes through the point (4, 2), so we can substitute these values into the equation to get:

2 = (-1/m)(4) + b

Step 2: Solve for b

To solve for b, we need to isolate it on one side of the equation. We can do this by multiplying both sides of the equation by m:

2m = -4 + mb

Step 3: Simplify the Equation

Now we can simplify the equation by combining like terms:

2m = mb - 4

Step 4: Add 4 to Both Sides of the Equation

To get rid of the negative term on the right-hand side of the equation, we can add 4 to both sides of the equation:

2m + 4 = mb

Step 5: Factor Out m

Now we can factor out m from the left-hand side of the equation:

m(2 + 4) = mb

Step 6: Simplify the Equation

Now we can simplify the equation by combining like terms:

6m = mb

Step 7: Divide Both Sides of the Equation by m

To solve for b, we need to isolate it on one side of the equation. We can do this by dividing both sides of the equation by m:

6 = b

Step 8: Write the Equation of the Line in Slope-Intercept Form

Now that we have the value of b, we can write the equation of the line in slope-intercept form:

y = (-1/m)x + 6

Step 9: Substitute the Value of m

Since we don't know the value of m, we can substitute the value of m into the equation:

y = (-1/(-1/m))x + 6

Step 10: Simplify the Equation

Now we can simplify the equation by combining like terms:

y = (m/m)x + 6

Step 11: Simplify the Equation

Now we can simplify the equation by combining like terms:

y = x + 6

Conclusion

In this article, we have shown how to find the equation of a line in slope-intercept form that is perpendicular to line G and passes through the point (4, 2). We have used the slope-intercept form of a line and the concept of perpendicular lines to find the equation of the line. We have also shown how to simplify the equation and write it in slope-intercept form.

Final Answer

The equation of the line in slope-intercept form that is perpendicular to line G and passes through the point (4, 2) is:

y = x + 6

Introduction

In our previous article, we showed how to find the equation of a line in slope-intercept form that is perpendicular to line G and passes through the point (4, 2). In this article, we will answer some frequently asked questions about the topic.

Q: What is the slope of the perpendicular line?

A: The slope of the perpendicular line is the negative reciprocal of the slope of line G. If the slope of line G is m, then the slope of the perpendicular line is -1/m.

Q: How do I find the equation of the perpendicular line?

A: To find the equation of the perpendicular line, you need to know the slope of line G and the point through which the line passes. You can use the slope-intercept form of a line and the concept of perpendicular lines to find the equation of the line.

Q: What is the equation of the line in slope-intercept form that is perpendicular to line G and passes through the point (4, 2)?

A: The equation of the line in slope-intercept form that is perpendicular to line G and passes through the point (4, 2) is:

y = x + 6

Q: How do I simplify the equation of the line?

A: To simplify the equation of the line, you can combine like terms and eliminate any negative terms.

Q: What is the y-intercept of the line?

A: The y-intercept of the line is 6.

Q: What is the x-intercept of the line?

A: To find the x-intercept of the line, you need to set y = 0 and solve for x. In this case, the x-intercept of the line is -6.

Q: How do I find the equation of a line that is parallel to line G?

A: To find the equation of a line that is parallel to line G, you need to know the slope of line G and the point through which the line passes. You can use the slope-intercept form of a line and the concept of parallel lines to find the equation of the line.

Q: What is the difference between a perpendicular line and a parallel line?

A: A perpendicular line is a line that intersects another line at a 90-degree angle, while a parallel line is a line that never intersects another line.

Q: How do I use the equation of a line to solve problems?

A: You can use the equation of a line to solve problems by substituting values into the equation and solving for the unknown variable.

Conclusion

In this article, we have answered some frequently asked questions about the equation of a line in slope-intercept form that is perpendicular to line G and passes through the point (4, 2). We have also provided some additional information about perpendicular lines and parallel lines.

Final Answer

The equation of the line in slope-intercept form that is perpendicular to line G and passes through the point (4, 2) is:

y = x + 6

The y-intercept of the line is 6, and the x-intercept of the line is -6.