Question

Identify the equation of a line in slope-intercept form that is perpendicular to y = -1/3 x + 2 and passes through (2, 1)

Answer 1

Answer:

Step-by-step explanation:

The slope of a line perpendicular to another line is the opposite reciprocal of the slope of the other line, meaning if the slope of the other line is $-\frac{1}{3}$, then the slope of the line perpendicular is $3$.

Knowing this, we can start to construct the equation for the line:

$y = mx + b$

$y = 3x + b$

To solve for $b$, we plug in the coordinates of the point that we know the line runs through, $(2, 1)$:

$y = 3x + b$

$1 = 3(2) + b$

$1 = 6 + b$

$b = -5$

Therefore, the slope of the line that is perpendicular ot the line provided in the equation is the following:

$y = 3x - 5$