Respuesta :
slope
Explanation
Step 1
Fin the slope of the line:
the function
[tex]y=-x-5[/tex]is written in the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ \text{where m is the slope} \end{gathered}[/tex]therefore, we can conclude
[tex]\begin{gathered} y=mx+b\rightarrow y=-x-5 \\ \text{slope}_1=m=-1 \end{gathered}[/tex]the solpe1 is -1
Now, we know that 2 lines are parallel if they have the same slope,
so
[tex]\begin{gathered} \text{ line 1 }\parallel\text{ line 2} \\ \text{then} \\ \text{slope}1=\text{slope}2 \\ -1=\text{slope}2 \end{gathered}[/tex]it means the slope of the line we are looking for is -1
Step 2
now, we have the slope and a point of the line, we can use
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \text{where m is the slope and } \\ (x_0,y_o)\text{ is a point of the line} \end{gathered}[/tex]then, let's replace
let P(3,2)
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ y-2=-1(x-3) \\ y-2=-x+3 \\ \text{add 2 in both sides} \\ y-2+2=-x+3+2 \\ y=-x+5 \end{gathered}[/tex]therefore, the equation is
[tex]y=-x+5[/tex]I hope this helps you
