A line that includes the points (-7, v) and (3, 1) has a slope of -1/10. What is the value of v?

Understand the Problem

The question is asking for the value of 'v' in the context of a line defined by two points, where the slope of the line is provided. We need to use the slope formula to find 'v'.

Answer

The value of $ v $ is $ 2 $.

Steps to Solve

Identify the given information We have two points: $(-7, v)$ and $(3, 1)$, and the slope of the line is $-\frac{1}{10}$.
Use the slope formula The slope formula is given by:

$$ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} $$

Here, $(x_1, y_1) = (-7, v)$ and $(x_2, y_2) = (3, 1)$.

Plug in the values to the slope formula Substituting the values into the slope formula:

$$ -\frac{1}{10} = \frac{1 - v}{3 - (-7)} $$

Simplify the denominator Calculate $3 - (-7)$:

$$ 3 + 7 = 10 $$

Thus, the equation updates to:

$$ -\frac{1}{10} = \frac{1 - v}{10} $$

Eliminate the denominator Multiply both sides by 10 to eliminate the fraction:

$$ -1 = 1 - v $$

Isolate 'v' To find the value of $v$, rearrange the equation:

$$ v = 1 + 1 $$

Calculate the final value of 'v' Thus,

$$ v = 2 $$

The value of ( v ) is ( 2 ).

More Information

This problem illustrates how to use the slope formula derived from two points on a line to find an unknown coordinate value.

Tips

Confusing the order of the points in the slope formula. Remember, ( (x_1, y_1) ) and ( (x_2, y_2) ) must be used consistently.
Forgetting to consider the negative sign of the slope when substituting values.

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

Thank you for voting!