The points (6, 0) and (2, v) fall on a line with a slope of 2. What is the value of v?

Understand the Problem

The question is asking for the value of 'v' in the coordinates of a point on a line with a specified slope. To find this, we can use the formula for the slope between two points and solve for 'v'.

Answer

The value of $ v $ is $ -8 $.

Steps to Solve

Identify the points and slope The points given are ( (6, 0) ) and ( (2, v) ). The slope of the line is given as ( 2 ).
Use the slope formula The formula for slope ( m ) between two points ( (x_1, y_1) ) and ( (x_2, y_2) ) is:

$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$

Substituting the given values:

$$ 2 = \frac{v - 0}{2 - 6} $$

Simplify the equation This simplifies to:

$$ 2 = \frac{v}{-4} $$

Solve for ( v ) Multiply both sides by ( -4 ):

$$ v = 2 \times -4 $$

Which simplifies to:

$$ v = -8 $$

The value of ( v ) is ( -8 ).

More Information

In this problem, we used the concept of slope to find the missing coordinate on a line. The slope represents the rate of change between two points, and it helps us determine the relationship between the coordinates.

Tips

Confusing the order of points in the slope formula can lead to incorrect results. Always make sure the points are in the correct position: ( (x_1, y_1) ) and ( (x_2, y_2) ).
Forgetting to multiply both sides of the equation by the denominator can cause errors in finding ( v ).

AI-generated content may contain errors. Please verify critical information

Thank you for voting!