In the plane, line  contains the points (-5,10) and  If the slope of line  is  what is the value of ?9 Mark For ReviewA) 2B) C) D)  -2

1. Break Down the Problem

To find the unknown point on the line given the slope and the point (-5, 10), we can use the slope formula. The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

2. Relevant Concepts

We have:

• Given point: $(-5, 10)$
• Slope ($m$) = -2
• Point to find: $(x_2, y_2)$

Assuming $(x_2, y_2)$ is the unknown point we want to determine, we can set up the equation using the slope formula.

3. Analysis and Detail

Substituting the known values into the slope formula:

$-2 = \frac{y_2 - 10}{x_2 + 5}$

Now we can express $y_2$ in terms of $x_2$:

$-2(x_2 + 5) = y_2 - 10$ $-2x_2 - 10 = y_2 - 10$ $y_2 = -2x_2$

4. Verify and Summarize

We can substitute this expression back to confirm consistency with the slope. Assuming $x_2 = 0$ for simplicity, calculate $y_2$:

$y_2 = -2 \cdot 0 = 0$

Thus, one possible line point could be $(0, 0)$.

Final Answer

If we take into account all provided options and the calculations, the answer should be determined by substituting into the slope equation accordingly and can yield multiple values depending on chosen $x_2$. However, none of the options provided are definitive without more specific information tied to particular values for either $x_2$ or $y_2$.