Question

Find the equation of the line through the line given points. (1, 6) and (-6, 6)

Answer 1

To solve the exercise we can first find the slope that passes through the given points using this formula

$\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}$

So, in this case, we have

$\begin{gathered} (x_1,y_1)=(1,6) \\ (x_2,y_2)=(-6,6) \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{6-6}{-6-1} \\ m=\frac{0}{-7} \\ m=0 \end{gathered}$

As this line has a slope of zero, then it is a horizontal line, which implies that y is constant, that is, and always takes the same value. Its equation is

$\begin{gathered} y=b\Rightarrow\text{ Equation of horizontal line} \\ \text{ Where b is the y coordinate of the y-intercept} \end{gathered}$

Therefore, the equation of the line through the line given points is

$y=6$

As you can see in the graph