Respuesta :
we are given points A and B that belong to a line and points B and C that belong to another line that is parallel to the first one. We will first find the line that goes through points B and C. First, we will find the slope of this line, using the following formula:
[tex]m_2=\frac{y_2-y_1}{x_2-x_1}[/tex]We have the following points:
[tex]\begin{gathered} (x_1,y_1)=(-5,9) \\ (x_2,y_2)=(5,4) \end{gathered}[/tex]replacing in the equation, we get:
[tex]m_2=\frac{4-9}{5-(-5)}=-\frac{5}{10}=-\frac{1}{2}[/tex]Since the lines are parallel, we have the following relationships between the slopes of each line:
[tex]m_1=-\frac{1}{m_2}[/tex]replacing the known values we get:
[tex]m_1=-\frac{1}{(-\frac{1}{2})}=2[/tex]Now we can apply the formula for the slope of these lines, using the following points:
[tex]\begin{gathered} (x_1,y_1)=(x,1) \\ (x_2,y_2)=(-3,7) \end{gathered}[/tex]Replacing the known values we get:
[tex]m_1=\frac{7-1}{-3-x}[/tex]replacing the value for the slope:
[tex]2=\frac{7-1}{-3-x}[/tex]Now we will solve for "x", first by solving the operation in the numerator:
[tex]2=\frac{6}{-3-x}[/tex]now we will multiply by the expression in the denominator on both sides:
[tex]2(-3-x)=\frac{6}{-3-x}(-3-x)[/tex]Simplifying:
[tex]-6-2x=6[/tex]Now we will add 6 on both sides:
[tex]\begin{gathered} -6+6-2x=6+6 \\ -2x=12 \end{gathered}[/tex]Now we will divide by "-2"
[tex]x=\frac{12}{-2}=-6[/tex]Therefore, the value of "x" for the two lines to be parallel is -6
