(4, 2) and (8, 1) (option D)
Explanation:
The given equation:
y = 4x - 1
comparing with equation of line:
y = mx + c
m = slope = 4
c = y-intercept = -1
For a line to be perpendicular to another line, the slope of one line will be the negative reciprocal of the other line.
We need to find the option which will give a negative reciprocal of 4.
[tex]slope=m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]
a) (1, -3) and (2, 1)
[tex]\begin{gathered} slope=\text{ }\frac{1-(-3)}{2-1}=\frac{1+3}{1}\text{ = }\frac{\text{4}}{1} \\ \text{slope = 4} \end{gathered}[/tex]
b) (-4, 7) and (-1, -5)
[tex]\begin{gathered} \text{slope = }\frac{-5-7}{-1-(-4)}=\frac{-5-7}{-1+4}=\frac{-12}{3} \\ \text{slope = -4} \end{gathered}[/tex]
c) (-8, -4) and (0, -2)
[tex]\begin{gathered} \text{slope = }\frac{-2-(-4)}{0-(-8)}=\frac{-2+4}{0+8}=\text{ }\frac{2}{8} \\ \text{slope = }\frac{1}{4} \end{gathered}[/tex]
d) (4, 2) and (8, 1)
[tex]\begin{gathered} \text{slope = }\frac{1-2}{8-4} \\ \text{slop}e\text{ }=\frac{-1}{4} \end{gathered}[/tex]
slope = 4
reciprocal of 4 = 1/4
negative reciprocal = - 1/4
Hence, the option whose slope gives the negative reciprocal of 4 is (4, 2) and (8, 1) (option D)
