Question

Which equation represents a line which is perpendicular to the line y= 2/7x – 6? O 2x + 7y = -56 O 7x - 2y = 6 O 7x + 2y = -8O 7y - 2x = 42

Answer 1

Th given equation of a line is in the slope intercept form;

`y=(2)/(7)x-6`

where the slope(m) is 2/7 and the intercept is -6.

For any line to be perpendicular to the above, its slope must be equal to the negative reciprocal of the slope of the line y= 2/7x – 6.

The reciprocal of the slope of y= 2/7x – 6 is -7/2.

So, let's go ahead and check each of the given lines to see which one has a slope of -7/2;

For line 2x + 7y = -56.

Let's write this in the slope intercept form;

`\begin{gathered} 7y=-2x-56 \\ \therefore y=(-2)/(7)x-8 \\ \end{gathered}`

The slope here is -2/7 which is not the required answer.

Let's pick the 7x - 2y = 6,

Writing this in the slope intercept form, we'll have;