Question

A line with a slope of m passes through the points (-2, -7) and (x, 1). What is the value of x?

A) x = -2
B) x = 0
C) x = 4
D) x = 6

Answer 1

The answer of the given equation that "A line with a slope of m passes through the points (-2, -7) and (x, 1). What is the value of x" is C) x = 4

Step-by-step explanation:

The formula for the slope (m) of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by:

`\[ m = \frac{{y₂ - y₁}}{{x₂ - x₁}} \]`

Given that the slope is \(m\) and one point is (-2, -7), we can substitute these values into the formula along with the other point (x, 1):

`\[ m = \frac{{1 - (-7)}}{{x - (-2)}} \]`

Simplifying this expression, we get:

`\[ m = \frac{8}{{x + 2}} \]`

Now, equate this expression to the given slope:

`\[ \frac{8}{{x + 2}} = m \]`

Since the given slope is
`\(m\)`, we substitute its value:

`\[ \frac{8}{{x + 2}} = m \]`

Now, solve for
`\(x\):`

`\[ 8 = m(x + 2) \]`

Since \(m\) is given as the slope, we can substitute its value:

`\[ 8 = \frac{{1 - (-7)}}{{x - (-2)}} \]`

Solving for
`\(x\):`

`\[ 8 = \frac{8}{{x + 2}} \]`

Multiply both sides by \(x + 2\):

`\[ 8(x + 2) = 8 \]`

Expand and simplify:

`\[ 8x + 16 = 8 \]`

Subtract 16 from both sides:

`\[ 8x = -8 \]`

Divide by 8:

`\[ x = -1 \]`

Therefore, the correct value of
`\(x\)` is -1. However, none of the given options match the correct value. There might be an error in the options provided or the question itself. If there is a typo in the question, and the correct value is indeed -1, none of the options accurately represents it.