Answer:
Therefore the value of p is -3.
Step-by-step explanation:
Given a line has a slope of [tex]-\frac{1}{7}[/tex] and passes through (4,-2)and (p,-1)
The slope of a line which passes through [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is
[tex]=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here [tex]x_1= 4,y_1=-2, x_2=p[/tex] and [tex]y_2= -1[/tex]
Therefore the slope of the line which passes through the given points is
[tex]=\frac{-1+2}{p-4}[/tex]
According to the problem,
[tex]\frac{-1+2}{p-4}= -\frac{1}{7}[/tex]
[tex]\Leftrightarrow \frac{1}{p-4} =-\frac{1}{7}[/tex]
[tex]\Leftrightarrow p-4=-7[/tex]
[tex]\Leftrightarrow p = -7+4[/tex]
[tex]\Leftrightarrow p = -3[/tex]
Therefore the value of p is -3.
