Respuesta :
Given:
Line a is parallel to line b.
Line a passes through the points (1,7) and (2,-4).
Line b passes through the point (6,14).
The objective is to find the equation of the line b in slope intercept form.
For parallel lines the slope of the two lines will be equal.
Consider the coordinates of the line a as,
[tex]\begin{gathered} (x_1,y_1)=(1,7) \\ (x_2,y_2)=(2,-4) \end{gathered}[/tex]The slope of line a can be calculated as,
[tex]\begin{gathered} m_a=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-4-7}{2-1} \\ =-11 \end{gathered}[/tex]Since both are given as parallel lines, the slop of line b will be,
[tex]m_b=-11[/tex]If the line b passes throught the point (6,14), the equation can be represented as,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-14=-11(x-6) \\ y-14=-11x+66 \\ y=-11x+66+14 \\ y=-11x+80 \end{gathered}[/tex]Hence, the equation of line b is y = -11x+80.
