Question

QuestionFind the equation of a line that contains the points (8, -1) and (-2, -1). Write the equation in slope-intercept form.

Answer 1

To solve the exercise, we can first find the slope of the line that passes through the given points. For this, we can use the following formula:

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

Then, we have:

$\begin{gathered} (x_1,y_1)=(8,-1) \\ (x_2,y_2)=(-2,-1) \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ m=\frac{-1-(-1)}{-2-8} \\ m=\frac{-1+1}{-10} \\ m=\frac{0}{-10} \\ m=0 \end{gathered}$

As you can see, the line has a slope of zero, that is, it is a horizontal line.

The equation of a horizontal line is:

$y=y_1_{}$

Where y₁ coincides with b, the y-intercept of the line.

Therefore, the equation in its slope-intercept form of the line containing the given points is:

$\boldsymbol{y=-1}$