Respuesta :
Solution:
The equation of a line passing through two points is expressed as
[tex]\begin{gathered} y-y_1=m\left(x-x_1\right)-----\text{ equation 1} \\ where \\ m\text{ is the slope of the line, which is expressed as} \\ m=\frac{y_2-y_1}{x_2-x_1}-----\text{ equation 2} \\ where \\ \left(x_1,y_1)\text{ and \lparen x}_2,y_2)\text{ are the coordinantes of the points through which}\right? \\ the\text{ line passes} \end{gathered}[/tex]Given that the line passes through the points (7,-9) and (9,-9), this implies that
[tex]\begin{gathered} x_1=7 \\ y_1=-9 \\ x_2=9 \\ y_2=-9 \end{gathered}[/tex]step 1: Evaluate the slope of the line.
Recall that the slope of the line is expressed as
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]Thus, the slope is evaluated to be
[tex]\begin{gathered} m=\frac{-9-\left(-9\right)}{9-7} \\ =\frac{-9+9}{9-7}=\frac{0}{2} \\ \Rightarrow m=0 \end{gathered}[/tex]Thus, the slope of the line is zero.
step 2: Express the equation of the line.
Since the slope of the line is evaluated to be zero, we have
[tex]\begin{gathered} y-y_{1}=m(x-x_{1}) \\ \Rightarrow y-\left(-9\right)=0\left(x-7\right) \\ open\text{ parentheses,} \\ y+9=0\text{ ---- equation 3} \\ \end{gathered}[/tex]In slope intercept form, the equation is expressed as
[tex]\begin{gathered} y=mx+c \\ where \\ m\text{ is the slope} \\ c\text{ is the y-intercept of the line} \end{gathered}[/tex]Thus, from equation 3, the equation in slope-intercept form becomes
[tex]\begin{gathered} y+9=0 \\ subtract\text{ 9 from both sides} \\ y+9-9=0-9 \\ \Rightarrow y=-9 \end{gathered}[/tex]Hence, the equation of the line in slope-intercept form is
[tex]y=-9[/tex]