Question

The line passinf through which two ordered pairs would be perpendicular tp the equation y=4x-1 ?

Answer 1

(4, 2) and (8, 1) (option D)

Step-by-step 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.

`slope=m\text{ = }(y_2-y_1)/(x_2-x_1)`

a) (1, -3) and (2, 1)

`\begin{gathered} slope=\text{ }(1-(-3))/(2-1)=(1+3)/(1)\text{ = }\frac{\text{4}}{1} \\ \text{slope = 4} \end{gathered}`

b) (-4, 7) and (-1, -5)

`\begin{gathered} \text{slope = }(-5-7)/(-1-(-4))=(-5-7)/(-1+4)=(-12)/(3) \\ \text{slope = -4} \end{gathered}`

c) (-8, -4) and (0, -2)

`\begin{gathered} \text{slope = }(-2-(-4))/(0-(-8))=(-2+4)/(0+8)=\text{ }(2)/(8) \\ \text{slope = }(1)/(4) \end{gathered}`

d) (4, 2) and (8, 1)

`\begin{gathered} \text{slope = }(1-2)/(8-4) \\ \text{slop}e\text{ }=(-1)/(4) \end{gathered}`

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)