Q. 24 - Geometry

Question

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

Step-by-Step Solution

Answer

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

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 to find the unknown x 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 unknown x coordinate is 3.