Question

Write an equation perpendicular to the line given and passes through the given point ( 6, -1).

HINT- Find the slope of the given line 1st
then write it in slope intercept form

Answer 1

The equation of the line perpendicular to the given line with slope 3 and passing through the point (6, -1) is y = (-1/3)x + 1.

Step-by-step explanation:

To write an equation for a line that is perpendicular to the given line and passes through the point (6, -1), we first need the slope of the given line. Using the details provided, we know the slope (m) of the given line is 3, and the y-intercept (b) is 9, which can be represented in slope-intercept form as y = 3x + 9. For a line to be perpendicular, its slope must be the negative reciprocal of the original slope. Therefore, the slope of the perpendicular line will be -1/3.

Now, we use the point-slope form to write the equation of the line that passes through the point (6, -1) with a slope of -1/3:

y - (-1) = (-1/3)(x - 6)

Simplifying this, we get:

y + 1 = (-1/3)x + 2

Subtracting 1 from both sides gives us the final slope-intercept form of the equation for the perpendicular line:

y = (-1/3)x + 1