Which Equation Represents The Line With A Slope Of $\frac{7}{3}$ That Passes Through The Point (4, -7)?A. $y + 7 = \frac{7}{3}(x - 4$\] B. $y - 7 = \frac{7}{3}(x - 4$\] C. $y + 4 = \frac{7}{3}(x + 7$\] D. $y - 4

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Which Equation Represents the Line with a Slope of 73\frac{7}{3} that Passes Through the Point (4, -7)?

In mathematics, a line can be represented by a linear equation in the form of y=mx+by = mx + b, where mm is the slope of the line and bb is the y-intercept. Given a point on the line and the slope, we can use the point-slope form of a linear equation to find the equation of the line. In this article, we will discuss how to find the equation of a line with a slope of 73\frac{7}{3} that passes through the point (4, -7).

Understanding the Point-Slope Form

The point-slope form of a linear equation is given by:

y−y1=m(x−x1)y - y_1 = m(x - x_1)

where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope of the line. This form is useful when we know a point on the line and the slope.

Finding the Equation of the Line

We are given that the slope of the line is 73\frac{7}{3} and the point (4, -7) lies on the line. We can use the point-slope form to find the equation of the line.

Let's substitute the values into the point-slope form:

y−(−7)=73(x−4)y - (-7) = \frac{7}{3}(x - 4)

Simplifying the equation, we get:

y+7=73(x−4)y + 7 = \frac{7}{3}(x - 4)

This is the equation of the line with a slope of 73\frac{7}{3} that passes through the point (4, -7).

Comparing with the Options

Now, let's compare the equation we found with the options given:

A. y+7=73(x−4)y + 7 = \frac{7}{3}(x - 4)

B. y−7=73(x−4)y - 7 = \frac{7}{3}(x - 4)

C. y+4=73(x+7)y + 4 = \frac{7}{3}(x + 7)

D. y−4=73(x−7)y - 4 = \frac{7}{3}(x - 7)

We can see that option A is the same as the equation we found.

In conclusion, the equation that represents the line with a slope of 73\frac{7}{3} that passes through the point (4, -7) is:

y+7=73(x−4)y + 7 = \frac{7}{3}(x - 4)

This equation can be used to find the y-coordinate of any point on the line, given the x-coordinate.

  • When using the point-slope form, make sure to substitute the values correctly.
  • Simplify the equation as much as possible to make it easier to read and understand.
  • Compare the equation you found with the options given to ensure you have the correct answer.
  • Q: What is the point-slope form of a linear equation? A: The point-slope form of a linear equation is given by y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope of the line.
  • Q: How do I find the equation of a line with a given slope and point? A: Use the point-slope form of a linear equation and substitute the values correctly.
  • Q: What is the equation of the line with a slope of 73\frac{7}{3} that passes through the point (4, -7)? A: The equation of the line is y+7=73(x−4)y + 7 = \frac{7}{3}(x - 4).
    Frequently Asked Questions: Point-Slope Form of a Linear Equation ====================================================================

In our previous article, we discussed how to find the equation of a line with a given slope and point using the point-slope form of a linear equation. In this article, we will answer some frequently asked questions related to the point-slope form.

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

A: The point-slope form of a linear equation is given by:

y−y1=m(x−x1)y - y_1 = m(x - x_1)

where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope of the line.

Q: How do I find the equation of a line with a given slope and point?

A: To find the equation of a line with a given slope and point, use the point-slope form of a linear equation and substitute the values correctly. For example, if the slope is 73\frac{7}{3} and the point is (4, -7), the equation would be:

y−(−7)=73(x−4)y - (-7) = \frac{7}{3}(x - 4)

Simplifying the equation, we get:

y+7=73(x−4)y + 7 = \frac{7}{3}(x - 4)

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

A: The point-slope form and the slope-intercept form are two different ways to represent a linear equation. The point-slope form is given by:

y−y1=m(x−x1)y - y_1 = m(x - x_1)

while the slope-intercept form is given by:

y=mx+by = mx + b

The slope-intercept form is more commonly used, but the point-slope form can be useful when we know a point on the line and the slope.

Q: Can I use the point-slope form to find the equation of a vertical line?

A: No, the point-slope form is not suitable for finding the equation of a vertical line. A vertical line has an undefined slope, and the point-slope form requires a defined slope.

Q: How do I find the equation of a line with a given point and a horizontal line?

A: To find the equation of a line with a given point and a horizontal line, use the point-slope form and substitute the values correctly. Since the line is horizontal, the slope is 0. For example, if the point is (4, -7) and the line is horizontal, the equation would be:

y−(−7)=0(x−4)y - (-7) = 0(x - 4)

Simplifying the equation, we get:

y=−7y = -7

Q: Can I use the point-slope form to find the equation of a line with a given slope and two points?

A: Yes, you can use the point-slope form to find the equation of a line with a given slope and two points. However, you will need to use the two points to find the equation of the line. For example, if the slope is 73\frac{7}{3} and the two points are (4, -7) and (6, -10), you can use the point-slope form to find the equation of the line.

In conclusion, the point-slope form of a linear equation is a useful tool for finding the equation of a line with a given slope and point. By understanding the point-slope form and how to use it, you can solve a variety of problems involving linear equations.

  • Make sure to substitute the values correctly when using the point-slope form.
  • Simplify the equation as much as possible to make it easier to read and understand.
  • Use the point-slope form to find the equation of a line with a given slope and point, and then compare it with the options given to ensure you have the correct answer.
  • Q: What is the point-slope form of a linear equation? A: The point-slope form of a linear equation is given by y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope of the line.
  • Q: How do I find the equation of a line with a given slope and point? A: Use the point-slope form of a linear equation and substitute the values correctly.
  • Q: What is the difference between the point-slope form and the slope-intercept form? A: The point-slope form and the slope-intercept form are two different ways to represent a linear equation. The point-slope form is given by y−y1=m(x−x1)y - y_1 = m(x - x_1), while the slope-intercept form is given by y=mx+by = mx + b.
  • Q: Can I use the point-slope form to find the equation of a vertical line? A: No, the point-slope form is not suitable for finding the equation of a vertical line.