Question

A line with slope$-\frac{5}{2}$ passes through points (7, -4) and (?, 6).

Short answer

A line with slope$-\frac{5}{2}$ passes through points$\left(7,-4\right)\text{and}\left(3,6\right)$

Step-by-step solution

Step-1 – Given

A line with slope$-\frac{5}{2}$ passes through points$\left(7,-4\right)\text{and}\left(?,6\right)$

Step-2 – To determine

We have tofind the unknownx coordinate of the given point.

Step-3 – Calculation 

The slope formula for two points$\left(x_1,y_1\right)$and$\left(x_2,y_2\right)$is:

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

The given points are$\left(7,-4\right)\text{and}\left(?,6\right)$.

Let = the unknown x coordinate

So,

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{y_2-y_1}{x_2-x_1}\\ -\frac{5}{2}=\frac{6-\left(-4\right)}{x_2-7}\\ -\frac{5}{2}=\frac{10}{x_2-7}\\ -5\left(x_2-7\right)=20\\ -5x_2+35=20\\ -5x_2=-15\\ x_2=3\end{array}$

Hence, the unknownx coordinate is 3.