Q. 23 - Geometry

Question

A line with slope  passes through points (2, 3) and (10, ?).

Step-by-Step Solution

Answer

A line with slope$\frac{3}{4}$  passes through points (2, 3) and (10, 6).

Step-1 – Given

A line with slope$\frac{3}{4}$  passes through points (2, 3) and (10, ?).

Step-2 – To determine

We have to find the unknown y 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 (2, 3) and (10, ?).

Let = the unknown y coordinate

So,

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ \frac{3}{4}=\frac{y_2-3}{10-2}\\ \frac{3}{4}=\frac{y_2-3}{8}\\ 24=4\left(y_2-3\right)\\ 24=4y_2-12\\ 4y_2=36\\ y_2=6\end{array}$

Hence, the unknown y coordinate is 6.